TY - CONF
AU - Ober-Blöbaum, Sina
AU - Vermeeren, M.
ID - 29421
T2 - 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC
TI - Superconvergence of galerkin variational integrators
VL - 54(19)
ER -
TY - JOUR
AB - Model predictive control is a prominent approach to construct a feedback
control loop for dynamical systems. Due to real-time constraints, the major
challenge in MPC is to solve model-based optimal control problems in a very
short amount of time. For linear-quadratic problems, Bemporad et al. have
proposed an explicit formulation where the underlying optimization problems are
solved a priori in an offline phase. In this article, we present an extension
of this concept in two significant ways. We consider nonlinear problems and -
more importantly - problems with multiple conflicting objective functions. In
the offline phase, we build a library of Pareto optimal solutions from which we
then obtain a valid compromise solution in the online phase according to a
decision maker's preference. Since the standard multi-parametric programming
approach is no longer valid in this situation, we instead use interpolation
between different entries of the library. To reduce the number of problems that
have to be solved in the offline phase, we exploit symmetries in the dynamical
system and the corresponding multiobjective optimal control problem. The
results are verified using two different examples from autonomous driving.
AU - Ober-Blöbaum, Sina
AU - Peitz, Sebastian
ID - 16294
JF - International Journal of Robust and Nonlinear Control
TI - Explicit multiobjective model predictive control for nonlinear systems with symmetries
VL - 31(2)
ER -
TY - JOUR
AU - Djema, Walid
AU - Giraldi, Laetitia
AU - Maslovskaya, Sofya
AU - Bernard, Olivier
ID - 29543
JF - Automatica
KW - Electrical and Electronic Engineering
KW - Control and Systems Engineering
SN - 0005-1098
TI - Turnpike features in optimal selection of species represented by quota models
VL - 132
ER -
TY - GEN
AB - In this article we prove meromorphic continuation of weighted zeta functions in the framework of open hyperbolic systems by using the meromorphically continued restricted resolvent of Dyatlov and Guillarmou (2016). We obtain a residue formula proving equality between residues of weighted zetas and invariant Ruelle distributions. We combine this equality with results of Guillarmou, Hilgert and Weich (2021) in order to relate the residues to Patterson-Sullivan distributions. Finally we provide proof-of-principle results concerning the numerical calculation of invariant Ruelle distributions for 3-disc scattering systems.
AU - Schütte, Philipp
AU - Weich, Tobias
AU - Barkhofen, Sonja
ID - 31059
TI - Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems
ER -
TY - GEN
AB - We consider a geodesic billiard system consisting of a complete Riemannian manifold and an obstacle submanifold with boundary at which the trajectories of the geodesic flow experience specular reflections. We show that if the geodesic billiard system is hyperbolic on its trapped set and the latter is compact and non-grazing the techniques for open hyperbolic systems developed by Dyatlov and Guillarmou can be applied to a smooth model for the discontinuous flow defined by the non-grazing billiard trajectories. This allows us to obtain a meromorphic resolvent for the generator of the billiard flow. As an application we prove a meromorphic continuation of weighted zeta functions together with explicit residue formulae. In particular, our results apply to scattering by convex obstacles in the Euclidean plane.
AU - Schütte, Philipp
AU - Weich, Tobias
AU - Delarue, Benjamin
ID - 31058
TI - Resonances and weighted zeta functions for obstacle scattering via smooth models
ER -
TY - JOUR
AU - Guillarmou, Colin
AU - Hilgert, Joachim
AU - Weich, Tobias
ID - 31263
JF - Annales Henri Lebesgue
SN - 2644-9463
TI - High frequency limits for invariant Ruelle densities
VL - 4
ER -
TY - GEN
AU - Hoffmann, Max
ID - 31385
T2 - Mathematische Semesterberichte
TI - Rezension: Hendrik Kasten und Denis Vogel: Grundlagen der ebenen Geometrie – Eine zugängliche aber exakte Einführung in die ebene Geometrie
VL - 68
ER -
TY - GEN
AB - For a compact Riemannian locally symmetric space $\Gamma\backslash G/K$ of
arbitrary rank we determine the location of certain Ruelle-Taylor resonances
for the Weyl chamber action. We provide a Weyl-lower bound on an appropriate
counting function for the Ruelle-Taylor resonances and establish a spectral gap
which is uniform in $\Gamma$ if $G/K$ is irreducible of higher rank. This is
achieved by proving a quantum-classical correspondence, i.e. a
1:1-correspondence between horocyclically invariant Ruelle-Taylor resonant
states and joint eigenfunctions of the algebra of invariant differential
operators on $G/K$.
AU - Hilgert, Joachim
AU - Weich, Tobias
AU - Wolf, Lasse Lennart
ID - 31190
T2 - arXiv:2103.05667
TI - Higher rank quantum-classical correspondence
ER -
TY - JOUR
AB - AbstractThe kinetic Brownian motion on the sphere bundle of a Riemannian manifold $$\mathbb {M}$$
M
is a stochastic process that models a random perturbation of the geodesic flow. If $$\mathbb {M}$$
M
is an orientable compact constantly curved surface, we show that in the limit of infinitely large perturbation the $$L^2$$
L
2
-spectrum of the infinitesimal generator of a time-rescaled version of the process converges to the Laplace spectrum of the base manifold.
AU - Kolb, Martin
AU - Weich, Tobias
AU - Wolf, Lasse Lennart
ID - 31193
IS - 4
JF - Annales Henri Poincaré
KW - Mathematical Physics
KW - Nuclear and High Energy Physics
KW - Statistical and Nonlinear Physics
SN - 1424-0637
TI - Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature
VL - 23
ER -
TY - CHAP
AU - Hoffmann, Max
ED - Biehler, Rolf
ED - Eichler, Andreas
ED - Hochmuth, Reinhard
ED - Rach, Stefanie
ED - Schaper, Niclas
ID - 31364
SN - 2197-8751
T2 - Lehrinnovationen in der Hochschulmathematik. praxisrelevant – didaktisch fundiert – forschungsbasiert
TI - Einsatz von Schnittstellenaufgaben in Mathematikveranstaltungen – Praxisbeispiele aus der Universität Paderborn
ER -
TY - GEN
AB - In this paper we complete the program of relating the Laplace spectrum for
rank one compact locally symmetric spaces with the first band Ruelle-Pollicott
resonances of the geodesic flow on its sphere bundle. This program was started
by Flaminio and Forni for hyperbolic surfaces, continued by Dyatlov, Faure and
Guillarmou for real hyperbolic spaces and by Guillarmou, Hilgert and Weich for
general rank one spaces. Except for the case of hyperbolic surfaces a countable
set of exceptional spectral parameters always left untreated since the
corresponding Poisson transforms are neither injective nor surjective. We use
vector valued Poisson transforms to treat also the exceptional spectral
parameters. For surfaces the exceptional spectral parameters lead to discrete
series representations of $\mathrm{SL}(2,\mathbb R)$. In higher dimensions the
situation is more complicated, but can be described completely.
AU - Arends, Christian
AU - Hilgert, Joachim
ID - 31210
T2 - arXiv:2112.11073
TI - Spectral Correspondences for Rank One Locally Symmetric Spaces -- The Case of Exceptional Parameters
ER -
TY - JOUR
AB - Abstract
For a compact Riemannian locally symmetric space $\mathcal M$ of rank 1 and an associated vector bundle $\mathbf V_{\tau }$ over the unit cosphere bundle $S^{\ast }\mathcal M$, we give a precise description of those classical (Pollicott–Ruelle) resonant states on $\mathbf V_{\tau }$ that vanish under covariant derivatives in the Anosov-unstable directions of the chaotic geodesic flow on $S^{\ast }\mathcal M$. In particular, we show that they are isomorphically mapped by natural pushforwards into generalized common eigenspaces of the algebra of invariant differential operators $D(G,\sigma )$ on compatible associated vector bundles $\mathbf W_{\sigma }$ over $\mathcal M$. As a consequence of this description, we obtain an exact band structure of the Pollicott–Ruelle spectrum. Further, under some mild assumptions on the representations $\tau$ and $\sigma$ defining the bundles $\mathbf V_{\tau }$ and $\mathbf W_{\sigma }$, we obtain a very explicit description of the generalized common eigenspaces. This allows us to relate classical Pollicott–Ruelle resonances to quantum eigenvalues of a Laplacian in a suitable Hilbert space of sections of $\mathbf W_{\sigma }$. Our methods of proof are based on representation theory and Lie theory.
AU - Küster, Benjamin
AU - Weich, Tobias
ID - 31261
IS - 11
JF - International Mathematics Research Notices
KW - General Mathematics
SN - 1073-7928
TI - Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces
VL - 2021
ER -
TY - JOUR
AU - Häsel-Weide, Uta
AU - Nührenbürger, Marcus
ID - 31576
IS - 14
JF - Zeitschrift für Grundschulforschung (ZfG)
TI - Inklusive Praktiken im Mathematikunterricht. Empirische Analysen von Unterrichtsdiskursen in Einführungsphasen.
ER -
TY - JOUR
AU - Häsel-Weide, Uta
AU - Seitz, Simone
AU - Wallner, Melina
AU - Wilke, Yannik
AU - Heckmann, Lara
ID - 31578
IS - 1
JF - QfI - Qualifizierung für Inklusion. Online-Zeitschrift zur Forschung über Aus-, Fort- und Weiterbildung pädagogischer Fachkräfte
TI - Mit Aufgaben im inklusiven Mathematikunterricht professionell umgehen - Erkenntnisse einer Interviewstudie mit Lehrpersonen der Sekundarstufe
VL - 3
ER -
TY - JOUR
AU - Häsel-Weide, Uta
AU - Schöttler, Christian
ID - 31577
IS - 2
JF - Zeitschrift für Mathematikdidaktik in Forschung & Praxis (ZMFP)
SN - 2701-9012
TI - Das Dezimalsystem verstehen – Bedeutung, Erkenntnisse, Anregungen
ER -
TY - CHAP
AU - Rezat, Sebastian
ED - Clark-Wilson, A.
ID - 31585
T2 - Mathematics Education in the Digital Age. Learning, Practice and Theory
TI - Challenges of making sense of tasks and automated feedback in digital mathematics textbooks
ER -
TY - JOUR
AU - Li, Jiaao
AU - Ma, Yulai
AU - Shi, Yongtang
AU - Wang, Weifan
AU - Wu, Yezhou
ID - 32810
JF - European Journal of Combinatorics
KW - Discrete Mathematics and Combinatorics
SN - 0195-6698
TI - On 3-flow-critical graphs
VL - 100
ER -
TY - JOUR
AB - The kinetic Brownian motion on the sphere bundle of a Riemannian manifold M is a stochastic process that models a random perturbation of the geodesic flow. If M is an orientable compact constantly curved surface, we show that in the limit of infinitely large perturbation the L2-spectrum of the infinitesimal generator of a time-rescaled version of the process converges to the Laplace spectrum of the base manifold.
AU - Kolb, Martin
AU - Weich, Tobias
AU - Wolf, Lasse
ID - 33278
IS - 4
JF - Annales Henri Poincaré
TI - Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature
VL - 23
ER -
TY - GEN
AU - Weich, Tobias
AU - Budde, Julia
ID - 32099
T2 - arXiv:2103.02968v1
TI - Wave Front Sets of Nilpotent Lie Group Representations
ER -
TY - GEN
AU - Weich, Tobias
AU - Guedes Bonthonneau, Yannick
AU - Guillarmou, Colin
ID - 32097
T2 - arXiv:2103.12127
TI - SRB Measures of Anosov Actions
ER -