@article{34904,
  abstract     = {{The purpose of this article is to determine all subfields ℚ(β) of fixed degree of a given algebraic number field ℚ(α). It is convenient to describe each subfield by a pair (h,g) of polynomials in ℚ[t] resp. Z[t] such thatgis the minimal polynomial of β = h(α). The computations are done in unramifiedp-adic extensions and use information concerning subgroups of the Galois group of the normal closure of ℚ(α) obtained from the van der Waerden criterion.}},
  author       = {{Klüners, Jürgen and Pohst, Michael}},
  issn         = {{0747-7171}},
  journal      = {{Journal of Symbolic Computation}},
  keywords     = {{Computational Mathematics, Algebra and Number Theory}},
  number       = {{3-4}},
  pages        = {{385--397}},
  publisher    = {{Elsevier BV}},
  title        = {{{On Computing Subfields}}},
  doi          = {{10.1006/jsco.1996.0140}},
  volume       = {{24}},
  year         = {{1997}},
}

@phdthesis{42806,
  author       = {{Klüners, Jürgen}},
  pages        = {{93}},
  title        = {{{Über die Berechnung von Automorphismen und Teilkörpern algebraischer Zahlkörper (Dissertation)}}},
  year         = {{1997}},
}

@inbook{16533,
  author       = {{Dellnitz, Michael and Hohmann, Andreas}},
  booktitle    = {{Nonlinear Dynamical Systems and Chaos}},
  isbn         = {{9783034875202}},
  title        = {{{The Computation of Unstable Manifolds Using Subdivision and Continuation}}},
  doi          = {{10.1007/978-3-0348-7518-9_21}},
  year         = {{1996}},
}

@article{16510,
  abstract     = {{<jats:p> In an array of coupled oscillators, synchronous chaos may occur in the sense that all the oscillators behave identically although the corresponding motion is chaotic. When a parameter is varied this fully symmetric dynamical state can lose its stability, and the main purpose of this paper is to investigate which type of dynamical behavior is expected to be observed once the loss of stability has occurred. The essential tool is a classification of Lyapunov exponents based on the symmetry of the underlying problem. This classification is crucial in the derivation of the analytical results but it also allows an efficient computation of the dominant Lyapunov exponent associated with each symmetry type. We show how these dominant exponents determine the stability of invariant sets possessing various instantaneous symmetries, and this leads to the idea of symmetry breaking bifurcations of chaotic attractors. Finally, the results and ideas are illustrated for several systems of coupled oscillators. </jats:p>}},
  author       = {{Aston, Philip J. and Dellnitz, Michael}},
  issn         = {{0218-1274}},
  journal      = {{International Journal of Bifurcation and Chaos}},
  pages        = {{1643--1676}},
  title        = {{{Symmetry Breaking Bifurcations of Chaotic Attractors}}},
  doi          = {{10.1142/s021812749500123x}},
  year         = {{1995}},
}

@article{16532,
  author       = {{Dellnitz, M and Heinrich, C}},
  issn         = {{0951-7715}},
  journal      = {{Nonlinearity}},
  pages        = {{1039--1066}},
  title        = {{{Admissible symmetry increasing bifurcations}}},
  doi          = {{10.1088/0951-7715/8/6/009}},
  year         = {{1995}},
}

@article{16542,
  author       = {{Dellnitz, M and Melbourne, I}},
  issn         = {{0951-7715}},
  journal      = {{Nonlinearity}},
  pages        = {{1067--1075}},
  title        = {{{A note on the shadowing lemma and symmetric periodic points}}},
  doi          = {{10.1088/0951-7715/8/6/010}},
  year         = {{1995}},
}

@article{16550,
  author       = {{Dellnitz, Michael and Field, Michael and Golubitsky, Martin and Ma, Jun and Hohmann, Andreas}},
  issn         = {{0218-1274}},
  journal      = {{International Journal of Bifurcation and Chaos}},
  pages        = {{1243--1247}},
  title        = {{{Cycling Chaos}}},
  doi          = {{10.1142/s0218127495000909}},
  year         = {{1995}},
}

@article{16551,
  abstract     = {{<jats:p> Spiral patterns have been observed experimentally, numerically, and theoretically in a variety of systems. It is often believed that these spiral wave patterns can occur only in systems of reaction–diffusion equations. We show, both theoretically (using Hopf bifurcation techniques) and numerically (using both direct simulation and continuation of rotating waves) that spiral wave patterns can appear in a single reaction–diffusion equation [ in u(x, t)] on a disk, if one assumes "spiral" boundary conditions (u<jats:sub>r</jats:sub> = mu<jats:sub>θ</jats:sub>). Spiral boundary conditions are motivated by assuming that a solution is infinitesimally an Archimedian spiral near the boundary. It follows from a bifurcation analysis that for this form of spirals there are no singularities in the spiral pattern (technically there is no spiral tip) and that at bifurcation there is a steep gradient between the "red" and "blue" arms of the spiral. </jats:p>}},
  author       = {{Dellnitz, Michael and Golubitsky, Martin and Hohmann, Andreas and Stewart, Ian}},
  issn         = {{0218-1274}},
  journal      = {{International Journal of Bifurcation and Chaos}},
  pages        = {{1487--1501}},
  title        = {{{Spirals in Scalar Reaction–Diffusion Equations}}},
  doi          = {{10.1142/s0218127495001149}},
  year         = {{1995}},
}

@inbook{16611,
  author       = {{Golubitsky, Martin and Marsden, Jerrold and Stewart, Ian and Dellnitz, Michael}},
  booktitle    = {{Normal Forms and Homoclinic Chaos}},
  isbn         = {{9780821803264}},
  title        = {{{The constrained Liapunov-Schmidt procedure and periodic orbits}}},
  doi          = {{10.1090/fic/004/05}},
  year         = {{1995}},
}

@misc{42808,
  author       = {{Klüners, Jürgen}},
  pages        = {{91}},
  title        = {{{Über die Berechnung von Teilkörpern algebraischer Zahlkörper (Diplomarbeit)}}},
  year         = {{1995}},
}

@article{16541,
  author       = {{Dellnitz, Michael and Melbourne, Ian}},
  issn         = {{0377-0427}},
  journal      = {{Journal of Computational and Applied Mathematics}},
  pages        = {{249--259}},
  title        = {{{Generic movement of eigenvalues for equivariant self-adjoint matrices}}},
  doi          = {{10.1016/0377-0427(94)90032-9}},
  year         = {{1994}},
}

@inbook{16544,
  author       = {{Dellnitz, Michael and Scheurle, Jürgen}},
  booktitle    = {{Dynamics, Bifurcation and Symmetry}},
  isbn         = {{9789401044134}},
  title        = {{{Eigenvalue Movement for a Class of Reversible Hamiltonian Systems with Three Degrees of Freedom}}},
  doi          = {{10.1007/978-94-011-0956-7_9}},
  year         = {{1994}},
}

@inbook{16549,
  author       = {{Dellnitz, Michael and Golubitsky, Martin and Nicol, Matthew}},
  booktitle    = {{Trends and Perspectives in Applied Mathematics}},
  isbn         = {{9781461269243}},
  issn         = {{0066-5452}},
  title        = {{{Symmetry of Attractors and the Karhunen-Loève Decomposition}}},
  doi          = {{10.1007/978-1-4612-0859-4_4}},
  year         = {{1994}},
}

@article{17014,
  author       = {{Dellnitz, Michael}},
  journal      = {{Schlaglichter der Forschung: Zum 75. Jahrestag der Universität Hamburg}},
  pages        = {{411--428}},
  title        = {{{Collisions of chaotic attractors}}},
  year         = {{1994}},
}

@article{16518,
  author       = {{Barany, Ernest and Dellnitz, Michael and Golubitsky, Martin}},
  issn         = {{0167-2789}},
  journal      = {{Physica D: Nonlinear Phenomena}},
  pages        = {{66--87}},
  title        = {{{Detecting the symmetry of attractors}}},
  doi          = {{10.1016/0167-2789(93)90198-a}},
  year         = {{1993}},
}

@article{16633,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>We obtain normal forms for infinitesimally symplectic matrices (or linear Hamiltonian vector fields) that commute with the symplectic action of a compact Lie group of symmetries. In doing so we extend Williamson's theorem on normal forms when there is no symmetry present.</jats:p><jats:p>Using standard representation-theoretic results the symmetry can be factored out and we reduce to finding normal forms over a real division ring. There are three real division rings consisting of the real, complex and quaternionic numbers. Of these, only the real case is covered in Williamson's original work.</jats:p>}},
  author       = {{Melbourne, Ian and Dellnitz, Michael}},
  issn         = {{0305-0041}},
  journal      = {{Mathematical Proceedings of the Cambridge Philosophical Society}},
  pages        = {{235--268}},
  title        = {{{Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group}}},
  doi          = {{10.1017/s0305004100071577}},
  year         = {{1993}},
}

@article{16634,
  author       = {{Melbourne, Ian and Dellnitz, Michael and Golubitsky, Martin}},
  issn         = {{0003-9527}},
  journal      = {{Archive for Rational Mechanics and Analysis}},
  pages        = {{75--98}},
  title        = {{{The structure of symmetric attractors}}},
  doi          = {{10.1007/bf00386369}},
  year         = {{1993}},
}

@article{17013,
  author       = {{Dellnitz, Michael}},
  journal      = {{Lectures in Applied Mathematics}},
  pages        = {{163--169}},
  title        = {{{The equivariant Darboux theorem}}},
  volume       = {{29}},
  year         = {{1993}},
}

@inbook{16546,
  author       = {{Dellnitz, Michael and Golubitsky, Martin and Melbourne, Ian}},
  booktitle    = {{Bifurcation and Symmetry}},
  isbn         = {{9783034875387}},
  title        = {{{Mechanisms of Symmetry Creation}}},
  doi          = {{10.1007/978-3-0348-7536-3_9}},
  year         = {{1992}},
}

@inbook{16547,
  author       = {{Dellnitz, Michael and Marsden, Jerrold E. and Melbourne, Ian and Scheurle, Jürgen}},
  booktitle    = {{Bifurcation and Symmetry}},
  isbn         = {{9783034875387}},
  title        = {{{Generic Bifurcations of Pendula}}},
  doi          = {{10.1007/978-3-0348-7536-3_10}},
  year         = {{1992}},
}