On manifolds of connecting orbits in discretizations of dynamical systems

DOI10.1016/S0362-546X(02)00269-9zbMath1018.37018OpenAlexW2093427279MaRDI QIDQ1863618

Wolf-Jürgen Beyn, Yongkui Zou

Publication date: 11 March 2003

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0362-546x(02)00269-9

zbMATH Keywords

dynamical systemsconnecting orbitstime discretizationhomoclinic tangenciesone-step methods

Mathematics Subject Classification ID

Numerical bifurcation problems (65P30) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

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Cites Work

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• The separation of motions in systems with rapidly rotating phase
• Dichotomies in stability theory
• Elements of applied bifurcation theory.
• The life-span of backward error analysis for numerical integrators
• Discretizations of dynamical systems with a saddle-node homoclinic orbit
• On the Hamiltonian interpolation of near-to-the-identity symplectic mappings with application to symplectic integration algorithms
• The Numerical Computation of Connecting Orbits in Dynamical Systems
• Stability of traveling waves: dichotomies and eigenvalue conditions on finite intervals
• Backward Error Analysis for Numerical Integrators
• The Numerical Computation of Homoclinic Orbits for Maps
• Approximation of solution branches of nonlinear equations
• Discretization of homoclinic orbits, rapid forcing and “invisible” chaos
• On C^j-closeness between the solution flow and its numerical approximation