---
_id: '63078'
abstract:
- lang: eng
  text: "For a finite group $G$, we describe the asymptotic growth of the number of\r\nconnected
    components of Hurwitz spaces of marked $G$-covers (of both the affine\r\nand projective
    lines) whose monodromy classes are constrained in a certain way,\r\nas the number
    of branch points grows to infinity. More precisely, we compute\r\nboth the exponent
    and (in many cases) the coefficient of the leading monomial\r\nin the count of
    components containing covers whose monodromy group is a given\r\nsubgroup of $G$.
    By the work of Ellenberg, Tran, Venkatesh and Westerland, this\r\nasymptotic behavior
    is related to the distribution of field extensions\r\nof~$\\mathbb{F}_q(T)$ with
    Galois group $G$."
author:
- first_name: Beranger Fabrice
  full_name: Seguin, Beranger Fabrice
  id: '102487'
  last_name: Seguin
citation:
  ama: Seguin BF. Counting Components of Hurwitz Spaces. <i>Israel Journal of Mathematics</i>.
    Published online 2025. doi:<a href="https://doi.org/10.1007/s11856-025-2848-5">10.1007/s11856-025-2848-5</a>
  apa: Seguin, B. F. (2025). Counting Components of Hurwitz Spaces. <i>Israel Journal
    of Mathematics</i>. <a href="https://doi.org/10.1007/s11856-025-2848-5">https://doi.org/10.1007/s11856-025-2848-5</a>
  bibtex: '@article{Seguin_2025, title={Counting Components of Hurwitz Spaces}, DOI={<a
    href="https://doi.org/10.1007/s11856-025-2848-5">10.1007/s11856-025-2848-5</a>},
    journal={Israel Journal of Mathematics}, publisher={Springer Science and Business
    Media LLC}, author={Seguin, Beranger Fabrice}, year={2025} }'
  chicago: Seguin, Beranger Fabrice. “Counting Components of Hurwitz Spaces.” <i>Israel
    Journal of Mathematics</i>, 2025. <a href="https://doi.org/10.1007/s11856-025-2848-5">https://doi.org/10.1007/s11856-025-2848-5</a>.
  ieee: 'B. F. Seguin, “Counting Components of Hurwitz Spaces,” <i>Israel Journal
    of Mathematics</i>, 2025, doi: <a href="https://doi.org/10.1007/s11856-025-2848-5">10.1007/s11856-025-2848-5</a>.'
  mla: Seguin, Beranger Fabrice. “Counting Components of Hurwitz Spaces.” <i>Israel
    Journal of Mathematics</i>, Springer Science and Business Media LLC, 2025, doi:<a
    href="https://doi.org/10.1007/s11856-025-2848-5">10.1007/s11856-025-2848-5</a>.
  short: B.F. Seguin, Israel Journal of Mathematics (2025).
date_created: 2025-12-12T23:09:07Z
date_updated: 2025-12-12T23:12:23Z
doi: 10.1007/s11856-025-2848-5
language:
- iso: eng
publication: Israel Journal of Mathematics
publication_identifier:
  issn:
  - 0021-2172
  - 1565-8511
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Counting Components of Hurwitz Spaces
type: journal_article
user_id: '102487'
year: '2025'
...
---
_id: '63262'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title><jats:p>Radially symmetric global unbounded
    solutions of the chemotaxis system <jats:disp-formula><jats:alternatives><jats:tex-math>$$\\left\\{
    {\\matrix{{{u_t} = \\nabla \\cdot (D(u)\\nabla u) - \\nabla \\cdot (uS(u)\\nabla
    v),} \\hfill &amp; {} \\hfill \\cr {0 = \\Delta v - \\mu + u,} \\hfill &amp; {\\mu
    = {1 \\over {|\\Omega |}}\\int_\\Omega {u,} } \\hfill \\cr } } \\right.$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n
    \                   <mml:mrow>\r\n                      <mml:mo>{</mml:mo>\r\n
    \                     <mml:mrow>\r\n                        <mml:mtable>\r\n                          <mml:mtr>\r\n
    \                           <mml:mtd>\r\n                              <mml:mrow>\r\n
    \                               <mml:msub>\r\n                                  <mml:mi>u</mml:mi>\r\n
    \                                 <mml:mi>t</mml:mi>\r\n                                </mml:msub>\r\n
    \                               <mml:mo>=</mml:mo>\r\n                                <mml:mo>∇</mml:mo>\r\n
    \                               <mml:mo>⋅</mml:mo>\r\n                                <mml:mo>(</mml:mo>\r\n
    \                               <mml:mi>D</mml:mi>\r\n                                <mml:mo>(</mml:mo>\r\n
    \                               <mml:mi>u</mml:mi>\r\n                                <mml:mo>)</mml:mo>\r\n
    \                               <mml:mo>∇</mml:mo>\r\n                                <mml:mi>u</mml:mi>\r\n
    \                               <mml:mo>)</mml:mo>\r\n                                <mml:mo>−</mml:mo>\r\n
    \                               <mml:mo>∇</mml:mo>\r\n                                <mml:mo>⋅</mml:mo>\r\n
    \                               <mml:mo>(</mml:mo>\r\n                                <mml:mi>u</mml:mi>\r\n
    \                               <mml:mi>S</mml:mi>\r\n                                <mml:mo>(</mml:mo>\r\n
    \                               <mml:mi>u</mml:mi>\r\n                                <mml:mo>)</mml:mo>\r\n
    \                               <mml:mo>∇</mml:mo>\r\n                                <mml:mi>v</mml:mi>\r\n
    \                               <mml:mo>)</mml:mo>\r\n                                <mml:mo>,</mml:mo>\r\n
    \                             </mml:mrow>\r\n                            </mml:mtd>\r\n
    \                           <mml:mtd>\r\n                              <mml:mrow/>\r\n
    \                           </mml:mtd>\r\n                          </mml:mtr>\r\n
    \                         <mml:mtr>\r\n                            <mml:mtd>\r\n
    \                             <mml:mrow>\r\n                                <mml:mn>0</mml:mn>\r\n
    \                               <mml:mo>=</mml:mo>\r\n                                <mml:mi>Δ</mml:mi>\r\n
    \                               <mml:mi>v</mml:mi>\r\n                                <mml:mo>−</mml:mo>\r\n
    \                               <mml:mi>μ</mml:mi>\r\n                                <mml:mo>+</mml:mo>\r\n
    \                               <mml:mi>u</mml:mi>\r\n                                <mml:mo>,</mml:mo>\r\n
    \                             </mml:mrow>\r\n                            </mml:mtd>\r\n
    \                           <mml:mtd>\r\n                              <mml:mrow>\r\n
    \                               <mml:mi>μ</mml:mi>\r\n                                <mml:mo>=</mml:mo>\r\n
    \                               <mml:mfrac>\r\n                                  <mml:mn>1</mml:mn>\r\n
    \                                 <mml:mrow>\r\n                                    <mml:mo>|</mml:mo>\r\n
    \                                   <mml:mi>Ω</mml:mi>\r\n                                    <mml:mo>|</mml:mo>\r\n
    \                                 </mml:mrow>\r\n                                </mml:mfrac>\r\n
    \                               <mml:mstyle>\r\n                                  <mml:mrow>\r\n
    \                                   <mml:msub>\r\n                                      <mml:mo>∫</mml:mo>\r\n
    \                                     <mml:mi>Ω</mml:mi>\r\n                                    </mml:msub>\r\n
    \                                   <mml:mrow>\r\n                                      <mml:mi>u</mml:mi>\r\n
    \                                     <mml:mo>,</mml:mo>\r\n                                    </mml:mrow>\r\n
    \                                 </mml:mrow>\r\n                                </mml:mstyle>\r\n
    \                             </mml:mrow>\r\n                            </mml:mtd>\r\n
    \                         </mml:mtr>\r\n                        </mml:mtable>\r\n
    \                     </mml:mrow>\r\n                    </mml:mrow>\r\n                  </mml:mrow>\r\n
    \               </mml:math></jats:alternatives></jats:disp-formula> are considered
    in a ball Ω = <jats:italic>B</jats:italic><jats:sub><jats:italic>R</jats:italic></jats:sub>(0)
    ⊂ ℝ<jats:sup><jats:italic>n</jats:italic></jats:sup>, where <jats:italic>n</jats:italic>
    ≥ 3 and <jats:italic>R</jats:italic> &gt; 0.</jats:p><jats:p>Under the assumption
    that <jats:italic>D</jats:italic> and <jats:italic>S</jats:italic> suitably generalize
    the prototypes given by <jats:italic>D</jats:italic>(<jats:italic>ξ</jats:italic>)
    = (<jats:italic>ξ</jats:italic> + <jats:italic>ι</jats:italic>)<jats:sup>m−1</jats:sup>
    and <jats:italic>S</jats:italic>(<jats:italic>ξ</jats:italic>) = (<jats:italic>ξ</jats:italic>
    + 1)<jats:sup>−λ−1</jats:sup> for all <jats:italic>ξ</jats:italic> &gt; 0 and
    some <jats:italic>m</jats:italic> ∈ ℝ, λ &gt;0 and <jats:italic>ι</jats:italic>
    ≥ 0 fulfilling <jats:inline-formula><jats:alternatives><jats:tex-math>$$m + \\lambda
    &lt; 1 - {2 \\over n}$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mi>m</mml:mi>\r\n                  <mml:mo>+</mml:mo>\r\n
    \                 <mml:mi>λ</mml:mi>\r\n                  <mml:mo>&lt;</mml:mo>\r\n
    \                 <mml:mn>1</mml:mn>\r\n                  <mml:mo>−</mml:mo>\r\n
    \                 <mml:mfrac>\r\n                    <mml:mn>2</mml:mn>\r\n                    <mml:mi>n</mml:mi>\r\n
    \                 </mml:mfrac>\r\n                </mml:math></jats:alternatives></jats:inline-formula>,
    a considerably large set of initial data <jats:italic>u</jats:italic><jats:sub>0</jats:sub>
    is found to enforce a complete mass aggregation in infinite time in the sense
    that for any such <jats:italic>u</jats:italic><jats:sub>0</jats:sub>, an associated
    Neumann type initial-boundary value problem admits a global classical solution
    (<jats:italic>u, v</jats:italic>) satisfying <jats:disp-formula><jats:alternatives><jats:tex-math>$${1
    \\over C} \\cdot {(t + 1)^{{1 \\over \\lambda }}} \\le ||u( \\cdot ,t)|{|_{{L^\\infty
    }(\\Omega )}} \\le C \\cdot {(t + 1)^{{1 \\over \\lambda }}}\\,\\,\\,{\\rm{for}}\\,\\,{\\rm{all}}\\,\\,t
    &gt; 0$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mrow>\r\n                    <mml:mfrac>\r\n                      <mml:mn>1</mml:mn>\r\n
    \                     <mml:mi>C</mml:mi>\r\n                    </mml:mfrac>\r\n
    \                 </mml:mrow>\r\n                  <mml:mo>⋅</mml:mo>\r\n                  <mml:mrow>\r\n
    \                   <mml:mo>(</mml:mo>\r\n                    <mml:mi>t</mml:mi>\r\n
    \                   <mml:mo>+</mml:mo>\r\n                    <mml:mn>1</mml:mn>\r\n
    \                   <mml:msup>\r\n                      <mml:mo>)</mml:mo>\r\n
    \                     <mml:mrow>\r\n                        <mml:mrow>\r\n                          <mml:mfrac>\r\n
    \                           <mml:mn>1</mml:mn>\r\n                            <mml:mi>λ</mml:mi>\r\n
    \                         </mml:mfrac>\r\n                        </mml:mrow>\r\n
    \                     </mml:mrow>\r\n                    </mml:msup>\r\n                  </mml:mrow>\r\n
    \                 <mml:mo>≤</mml:mo>\r\n                  <mml:mrow>\r\n                    <mml:mo>|</mml:mo>\r\n
    \                 </mml:mrow>\r\n                  <mml:mrow>\r\n                    <mml:mo>|</mml:mo>\r\n
    \                 </mml:mrow>\r\n                  <mml:mi>u</mml:mi>\r\n                  <mml:mo>(</mml:mo>\r\n
    \                 <mml:mo>⋅</mml:mo>\r\n                  <mml:mo>,</mml:mo>\r\n
    \                 <mml:mi>t</mml:mi>\r\n                  <mml:mo>)</mml:mo>\r\n
    \                 <mml:mrow>\r\n                    <mml:mo>|</mml:mo>\r\n                  </mml:mrow>\r\n
    \                 <mml:mrow>\r\n                    <mml:msub>\r\n                      <mml:mrow>\r\n
    \                       <mml:mo>|</mml:mo>\r\n                      </mml:mrow>\r\n
    \                     <mml:mrow>\r\n                        <mml:mrow>\r\n                          <mml:msup>\r\n
    \                           <mml:mi>L</mml:mi>\r\n                            <mml:mi>∞</mml:mi>\r\n
    \                         </mml:msup>\r\n                        </mml:mrow>\r\n
    \                       <mml:mo>(</mml:mo>\r\n                        <mml:mi>Ω</mml:mi>\r\n
    \                       <mml:mo>)</mml:mo>\r\n                      </mml:mrow>\r\n
    \                   </mml:msub>\r\n                  </mml:mrow>\r\n                  <mml:mo>≤</mml:mo>\r\n
    \                 <mml:mi>C</mml:mi>\r\n                  <mml:mo>⋅</mml:mo>\r\n
    \                 <mml:mrow>\r\n                    <mml:mo>(</mml:mo>\r\n                    <mml:mi>t</mml:mi>\r\n
    \                   <mml:mo>+</mml:mo>\r\n                    <mml:mn>1</mml:mn>\r\n
    \                   <mml:msup>\r\n                      <mml:mo>)</mml:mo>\r\n
    \                     <mml:mrow>\r\n                        <mml:mrow>\r\n                          <mml:mfrac>\r\n
    \                           <mml:mn>1</mml:mn>\r\n                            <mml:mi>λ</mml:mi>\r\n
    \                         </mml:mfrac>\r\n                        </mml:mrow>\r\n
    \                     </mml:mrow>\r\n                    </mml:msup>\r\n                  </mml:mrow>\r\n
    \                 <mml:mspace/>\r\n                  <mml:mspace/>\r\n                  <mml:mspace/>\r\n
    \                 <mml:mrow>\r\n                    <mml:mrow>\r\n                      <mml:mi>f</mml:mi>\r\n
    \                     <mml:mi>o</mml:mi>\r\n                      <mml:mi>r</mml:mi>\r\n
    \                   </mml:mrow>\r\n                  </mml:mrow>\r\n                  <mml:mspace/>\r\n
    \                 <mml:mspace/>\r\n                  <mml:mrow>\r\n                    <mml:mrow>\r\n
    \                     <mml:mi>a</mml:mi>\r\n                      <mml:mi>l</mml:mi>\r\n
    \                     <mml:mi>l</mml:mi>\r\n                    </mml:mrow>\r\n
    \                 </mml:mrow>\r\n                  <mml:mspace/>\r\n                  <mml:mspace/>\r\n
    \                 <mml:mi>t</mml:mi>\r\n                  <mml:mo>&gt;</mml:mo>\r\n
    \                 <mml:mn>0</mml:mn>\r\n                </mml:math></jats:alternatives></jats:disp-formula>
    as well as <jats:disp-formula><jats:alternatives><jats:tex-math>$$||u( \\cdot
    \\,,t)|{|_{{L^1}(\\Omega \\backslash {B_{{r_0}}}(0))}} \\to 0\\,\\,\\,{\\rm{as}}\\,\\,t
    \\to \\infty \\,\\,\\,{\\rm{for}}\\,\\,{\\rm{all}}\\,\\,{r_0} \\in (0,R)$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mo>|</mml:mo>\r\n
    \                 <mml:mo>|</mml:mo>\r\n                  <mml:mi>u</mml:mi>\r\n
    \                 <mml:mo>(</mml:mo>\r\n                  <mml:mo>⋅</mml:mo>\r\n
    \                 <mml:mo>,</mml:mo>\r\n                  <mml:mi>t</mml:mi>\r\n
    \                 <mml:mo>)</mml:mo>\r\n                  <mml:mo>|</mml:mo>\r\n
    \                 <mml:msub>\r\n                    <mml:mo>|</mml:mo>\r\n                    <mml:mrow>\r\n
    \                     <mml:msup>\r\n                        <mml:mi>L</mml:mi>\r\n
    \                       <mml:mn>1</mml:mn>\r\n                      </mml:msup>\r\n
    \                     <mml:mo>(</mml:mo>\r\n                      <mml:mi>Ω</mml:mi>\r\n
    \                     <mml:mo>\\</mml:mo>\r\n                      <mml:msub>\r\n
    \                       <mml:mi>B</mml:mi>\r\n                        <mml:mrow>\r\n
    \                         <mml:msub>\r\n                            <mml:mi>r</mml:mi>\r\n
    \                           <mml:mn>0</mml:mn>\r\n                          </mml:msub>\r\n
    \                       </mml:mrow>\r\n                      </mml:msub>\r\n                      <mml:mo>(</mml:mo>\r\n
    \                     <mml:mn>0</mml:mn>\r\n                      <mml:mo>)</mml:mo>\r\n
    \                     <mml:mo>)</mml:mo>\r\n                    </mml:mrow>\r\n
    \                 </mml:msub>\r\n                  <mml:mo>→</mml:mo>\r\n                  <mml:mn>0</mml:mn>\r\n
    \                 <mml:mtext>as</mml:mtext>\r\n                  <mml:mi>t</mml:mi>\r\n
    \                 <mml:mo>→</mml:mo>\r\n                  <mml:mi>∞</mml:mi>\r\n
    \                 <mml:mtext>for all</mml:mtext>\r\n                  <mml:msub>\r\n
    \                   <mml:mi>r</mml:mi>\r\n                    <mml:mn>0</mml:mn>\r\n
    \                 </mml:msub>\r\n                  <mml:mo>∈</mml:mo>\r\n                  <mml:mo>(</mml:mo>\r\n
    \                 <mml:mn>0</mml:mn>\r\n                  <mml:mo>,</mml:mo>\r\n
    \                 <mml:mi>R</mml:mi>\r\n                  <mml:mo>)</mml:mo>\r\n
    \               </mml:math></jats:alternatives></jats:disp-formula> with some
    <jats:italic>C</jats:italic> &gt; 0.</jats:p>"
author:
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Winkler M. Complete infinite-time mass aggregation in a quasilinear Keller–Segel
    system. <i>Israel Journal of Mathematics</i>. 2024;263(1):93-127. doi:<a href="https://doi.org/10.1007/s11856-024-2618-9">10.1007/s11856-024-2618-9</a>
  apa: Winkler, M. (2024). Complete infinite-time mass aggregation in a quasilinear
    Keller–Segel system. <i>Israel Journal of Mathematics</i>, <i>263</i>(1), 93–127.
    <a href="https://doi.org/10.1007/s11856-024-2618-9">https://doi.org/10.1007/s11856-024-2618-9</a>
  bibtex: '@article{Winkler_2024, title={Complete infinite-time mass aggregation in
    a quasilinear Keller–Segel system}, volume={263}, DOI={<a href="https://doi.org/10.1007/s11856-024-2618-9">10.1007/s11856-024-2618-9</a>},
    number={1}, journal={Israel Journal of Mathematics}, publisher={Springer Science
    and Business Media LLC}, author={Winkler, Michael}, year={2024}, pages={93–127}
    }'
  chicago: 'Winkler, Michael. “Complete Infinite-Time Mass Aggregation in a Quasilinear
    Keller–Segel System.” <i>Israel Journal of Mathematics</i> 263, no. 1 (2024):
    93–127. <a href="https://doi.org/10.1007/s11856-024-2618-9">https://doi.org/10.1007/s11856-024-2618-9</a>.'
  ieee: 'M. Winkler, “Complete infinite-time mass aggregation in a quasilinear Keller–Segel
    system,” <i>Israel Journal of Mathematics</i>, vol. 263, no. 1, pp. 93–127, 2024,
    doi: <a href="https://doi.org/10.1007/s11856-024-2618-9">10.1007/s11856-024-2618-9</a>.'
  mla: Winkler, Michael. “Complete Infinite-Time Mass Aggregation in a Quasilinear
    Keller–Segel System.” <i>Israel Journal of Mathematics</i>, vol. 263, no. 1, Springer
    Science and Business Media LLC, 2024, pp. 93–127, doi:<a href="https://doi.org/10.1007/s11856-024-2618-9">10.1007/s11856-024-2618-9</a>.
  short: M. Winkler, Israel Journal of Mathematics 263 (2024) 93–127.
date_created: 2025-12-18T19:08:34Z
date_updated: 2025-12-18T20:14:59Z
doi: 10.1007/s11856-024-2618-9
intvolume: '       263'
issue: '1'
language:
- iso: eng
page: 93-127
publication: Israel Journal of Mathematics
publication_identifier:
  issn:
  - 0021-2172
  - 1565-8511
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Complete infinite-time mass aggregation in a quasilinear Keller–Segel system
type: journal_article
user_id: '31496'
volume: 263
year: '2024'
...
---
_id: '63352'
author:
- first_name: Johannes
  full_name: Lankeit, Johannes
  last_name: Lankeit
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Lankeit J, Winkler M. Counterintuitive dependence of temporal asymptotics on
    initial decay in a nonlocal degenerate parabolic equation arising in game theory.
    <i>Israel Journal of Mathematics</i>. 2019;233(1):249-296. doi:<a href="https://doi.org/10.1007/s11856-019-1900-8">10.1007/s11856-019-1900-8</a>
  apa: Lankeit, J., &#38; Winkler, M. (2019). Counterintuitive dependence of temporal
    asymptotics on initial decay in a nonlocal degenerate parabolic equation arising
    in game theory. <i>Israel Journal of Mathematics</i>, <i>233</i>(1), 249–296.
    <a href="https://doi.org/10.1007/s11856-019-1900-8">https://doi.org/10.1007/s11856-019-1900-8</a>
  bibtex: '@article{Lankeit_Winkler_2019, title={Counterintuitive dependence of temporal
    asymptotics on initial decay in a nonlocal degenerate parabolic equation arising
    in game theory}, volume={233}, DOI={<a href="https://doi.org/10.1007/s11856-019-1900-8">10.1007/s11856-019-1900-8</a>},
    number={1}, journal={Israel Journal of Mathematics}, publisher={Springer Science
    and Business Media LLC}, author={Lankeit, Johannes and Winkler, Michael}, year={2019},
    pages={249–296} }'
  chicago: 'Lankeit, Johannes, and Michael Winkler. “Counterintuitive Dependence of
    Temporal Asymptotics on Initial Decay in a Nonlocal Degenerate Parabolic Equation
    Arising in Game Theory.” <i>Israel Journal of Mathematics</i> 233, no. 1 (2019):
    249–96. <a href="https://doi.org/10.1007/s11856-019-1900-8">https://doi.org/10.1007/s11856-019-1900-8</a>.'
  ieee: 'J. Lankeit and M. Winkler, “Counterintuitive dependence of temporal asymptotics
    on initial decay in a nonlocal degenerate parabolic equation arising in game theory,”
    <i>Israel Journal of Mathematics</i>, vol. 233, no. 1, pp. 249–296, 2019, doi:
    <a href="https://doi.org/10.1007/s11856-019-1900-8">10.1007/s11856-019-1900-8</a>.'
  mla: Lankeit, Johannes, and Michael Winkler. “Counterintuitive Dependence of Temporal
    Asymptotics on Initial Decay in a Nonlocal Degenerate Parabolic Equation Arising
    in Game Theory.” <i>Israel Journal of Mathematics</i>, vol. 233, no. 1, Springer
    Science and Business Media LLC, 2019, pp. 249–96, doi:<a href="https://doi.org/10.1007/s11856-019-1900-8">10.1007/s11856-019-1900-8</a>.
  short: J. Lankeit, M. Winkler, Israel Journal of Mathematics 233 (2019) 249–296.
date_created: 2025-12-19T10:51:24Z
date_updated: 2025-12-19T10:51:33Z
doi: 10.1007/s11856-019-1900-8
intvolume: '       233'
issue: '1'
language:
- iso: eng
page: 249-296
publication: Israel Journal of Mathematics
publication_identifier:
  issn:
  - 0021-2172
  - 1565-8511
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Counterintuitive dependence of temporal asymptotics on initial decay in a nonlocal
  degenerate parabolic equation arising in game theory
type: journal_article
user_id: '31496'
volume: 233
year: '2019'
...
---
_id: '64631'
article_type: original
author:
- first_name: Timothy P.
  full_name: Bywaters, Timothy P.
  last_name: Bywaters
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
- first_name: Stephan
  full_name: Tornier, Stephan
  last_name: Tornier
citation:
  ama: Bywaters TP, Glöckner H, Tornier S. Contraction groups and passage to subgroups
    and quotients for endomorphisms of totally disconnected locally compact groups.
    <i>Israel Journal of Mathematics</i>. 2018;227(2):691–752. doi:<a href="https://doi.org/10.1007/s11856-018-1750-9">10.1007/s11856-018-1750-9</a>
  apa: Bywaters, T. P., Glöckner, H., &#38; Tornier, S. (2018). Contraction groups
    and passage to subgroups and quotients for endomorphisms of totally disconnected
    locally compact groups. <i>Israel Journal of Mathematics</i>, <i>227</i>(2), 691–752.
    <a href="https://doi.org/10.1007/s11856-018-1750-9">https://doi.org/10.1007/s11856-018-1750-9</a>
  bibtex: '@article{Bywaters_Glöckner_Tornier_2018, title={Contraction groups and
    passage to subgroups and quotients for endomorphisms of totally disconnected locally
    compact groups}, volume={227}, DOI={<a href="https://doi.org/10.1007/s11856-018-1750-9">10.1007/s11856-018-1750-9</a>},
    number={2}, journal={Israel Journal of Mathematics}, author={Bywaters, Timothy
    P. and Glöckner, Helge and Tornier, Stephan}, year={2018}, pages={691–752} }'
  chicago: 'Bywaters, Timothy P., Helge Glöckner, and Stephan Tornier. “Contraction
    Groups and Passage to Subgroups and Quotients for Endomorphisms of Totally Disconnected
    Locally Compact Groups.” <i>Israel Journal of Mathematics</i> 227, no. 2 (2018):
    691–752. <a href="https://doi.org/10.1007/s11856-018-1750-9">https://doi.org/10.1007/s11856-018-1750-9</a>.'
  ieee: 'T. P. Bywaters, H. Glöckner, and S. Tornier, “Contraction groups and passage
    to subgroups and quotients for endomorphisms of totally disconnected locally compact
    groups,” <i>Israel Journal of Mathematics</i>, vol. 227, no. 2, pp. 691–752, 2018,
    doi: <a href="https://doi.org/10.1007/s11856-018-1750-9">10.1007/s11856-018-1750-9</a>.'
  mla: Bywaters, Timothy P., et al. “Contraction Groups and Passage to Subgroups and
    Quotients for Endomorphisms of Totally Disconnected Locally Compact Groups.” <i>Israel
    Journal of Mathematics</i>, vol. 227, no. 2, 2018, pp. 691–752, doi:<a href="https://doi.org/10.1007/s11856-018-1750-9">10.1007/s11856-018-1750-9</a>.
  short: T.P. Bywaters, H. Glöckner, S. Tornier, Israel Journal of Mathematics 227
    (2018) 691–752.
date_created: 2026-02-26T07:06:47Z
date_updated: 2026-02-27T08:33:34Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.1007/s11856-018-1750-9
intvolume: '       227'
issue: '2'
keyword:
- '22E10'
- 47H09
- 54H11
language:
- iso: eng
page: 691–752
publication: Israel Journal of Mathematics
publication_identifier:
  issn:
  - 0021-2172
quality_controlled: '1'
status: public
title: Contraction groups and passage to subgroups and quotients for endomorphisms
  of totally disconnected locally compact groups
type: journal_article
user_id: '178'
volume: 227
year: '2018'
...
---
_id: '64679'
article_type: original
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
- first_name: Ralf
  full_name: Gramlich, Ralf
  last_name: Gramlich
- first_name: Tobias
  full_name: Hartnick, Tobias
  last_name: Hartnick
citation:
  ama: Glöckner H, Gramlich R, Hartnick T. Final group topologies, Kac-Moody groups
    and Pontryagin duality. <i>Israel Journal of Mathematics</i>. 2010;177:49–101.
    doi:<a href="https://doi.org/10.1007/s11856-010-0038-5">10.1007/s11856-010-0038-5</a>
  apa: Glöckner, H., Gramlich, R., &#38; Hartnick, T. (2010). Final group topologies,
    Kac-Moody groups and Pontryagin duality. <i>Israel Journal of Mathematics</i>,
    <i>177</i>, 49–101. <a href="https://doi.org/10.1007/s11856-010-0038-5">https://doi.org/10.1007/s11856-010-0038-5</a>
  bibtex: '@article{Glöckner_Gramlich_Hartnick_2010, title={Final group topologies,
    Kac-Moody groups and Pontryagin duality}, volume={177}, DOI={<a href="https://doi.org/10.1007/s11856-010-0038-5">10.1007/s11856-010-0038-5</a>},
    journal={Israel Journal of Mathematics}, author={Glöckner, Helge and Gramlich,
    Ralf and Hartnick, Tobias}, year={2010}, pages={49–101} }'
  chicago: 'Glöckner, Helge, Ralf Gramlich, and Tobias Hartnick. “Final Group Topologies,
    Kac-Moody Groups and Pontryagin Duality.” <i>Israel Journal of Mathematics</i>
    177 (2010): 49–101. <a href="https://doi.org/10.1007/s11856-010-0038-5">https://doi.org/10.1007/s11856-010-0038-5</a>.'
  ieee: 'H. Glöckner, R. Gramlich, and T. Hartnick, “Final group topologies, Kac-Moody
    groups and Pontryagin duality,” <i>Israel Journal of Mathematics</i>, vol. 177,
    pp. 49–101, 2010, doi: <a href="https://doi.org/10.1007/s11856-010-0038-5">10.1007/s11856-010-0038-5</a>.'
  mla: Glöckner, Helge, et al. “Final Group Topologies, Kac-Moody Groups and Pontryagin
    Duality.” <i>Israel Journal of Mathematics</i>, vol. 177, 2010, pp. 49–101, doi:<a
    href="https://doi.org/10.1007/s11856-010-0038-5">10.1007/s11856-010-0038-5</a>.
  short: H. Glöckner, R. Gramlich, T. Hartnick, Israel Journal of Mathematics 177
    (2010) 49–101.
date_created: 2026-02-26T11:13:32Z
date_updated: 2026-02-27T08:23:45Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.1007/s11856-010-0038-5
intvolume: '       177'
keyword:
- '22E65'
language:
- iso: eng
page: 49–101
publication: Israel Journal of Mathematics
publication_identifier:
  issn:
  - 0021-2172
quality_controlled: '1'
status: public
title: Final group topologies, Kac-Moody groups and Pontryagin duality
type: journal_article
user_id: '178'
volume: 177
year: '2010'
...
---
_id: '64694'
article_type: original
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
citation:
  ama: Glöckner H. Implicit functions from topological vector spaces to Banach spaces.
    <i>Israel Journal of Mathematics</i>. 2006;155:205–252. doi:<a href="https://doi.org/10.1007/BF02773955">10.1007/BF02773955</a>
  apa: Glöckner, H. (2006). Implicit functions from topological vector spaces to Banach
    spaces. <i>Israel Journal of Mathematics</i>, <i>155</i>, 205–252. <a href="https://doi.org/10.1007/BF02773955">https://doi.org/10.1007/BF02773955</a>
  bibtex: '@article{Glöckner_2006, title={Implicit functions from topological vector
    spaces to Banach spaces}, volume={155}, DOI={<a href="https://doi.org/10.1007/BF02773955">10.1007/BF02773955</a>},
    journal={Israel Journal of Mathematics}, author={Glöckner, Helge}, year={2006},
    pages={205–252} }'
  chicago: 'Glöckner, Helge. “Implicit Functions from Topological Vector Spaces to
    Banach Spaces.” <i>Israel Journal of Mathematics</i> 155 (2006): 205–252. <a href="https://doi.org/10.1007/BF02773955">https://doi.org/10.1007/BF02773955</a>.'
  ieee: 'H. Glöckner, “Implicit functions from topological vector spaces to Banach
    spaces,” <i>Israel Journal of Mathematics</i>, vol. 155, pp. 205–252, 2006, doi:
    <a href="https://doi.org/10.1007/BF02773955">10.1007/BF02773955</a>.'
  mla: Glöckner, Helge. “Implicit Functions from Topological Vector Spaces to Banach
    Spaces.” <i>Israel Journal of Mathematics</i>, vol. 155, 2006, pp. 205–252, doi:<a
    href="https://doi.org/10.1007/BF02773955">10.1007/BF02773955</a>.
  short: H. Glöckner, Israel Journal of Mathematics 155 (2006) 205–252.
date_created: 2026-02-26T11:50:44Z
date_updated: 2026-02-27T08:00:51Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.1007/BF02773955
extern: '1'
intvolume: '       155'
keyword:
- 47J07
- 47S10
- 58B10
- 58C15
- 46T05
language:
- iso: eng
page: 205–252
publication: Israel Journal of Mathematics
publication_identifier:
  issn:
  - 0021-2172
quality_controlled: '1'
status: public
title: Implicit functions from topological vector spaces to Banach spaces
type: journal_article
user_id: '178'
volume: 155
year: '2006'
...