Transversal homoclinic points and hyperbolic sets for non-autonomous maps. II

DOI10.1007/BF00945119zbMath0692.58032OpenAlexW4247784894MaRDI QIDQ583682

Daniel Stoffer

Publication date: 1988

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00945119

zbMATH Keywords

existencehyperbolic setsalmost perturbed differential equationstransverse homoclinic orbits

Mathematics Subject Classification ID

Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50) Dynamical systems with hyperbolic orbits and sets (37D05) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Topological dynamics of nonautonomous systems (37B55)

Related Items (13)

Chaotic motions near homoclinic manifolds and resonant tori in quasiperiodic perturbations of planar Hamiltonian systems ⋮ New global bifurcation diagrams for piecewise smooth systems: transversality of homoclinic points does not imply chaos ⋮ Invariant manifold templates for chaotic advection ⋮ Melnikov processes and chaos in randomly perturbed dynamical systems ⋮ Chaotic Dynamics in Nonautonomous Maps: Application to the Nonautonomous Hénon Map ⋮ Transversal homoclinic points and hyperbolic sets for non-autonomous maps. I ⋮ Nonautonomous gradient-like vector fields on the circle: classification, structural stability and autonomization ⋮ Computation of stable and unstable manifolds of hyperbolic trajectories in two-dimensional, aperiodically time-dependent vector fields ⋮ On the position of chaotic trajectories ⋮ Invariant manifolds and control of hyperbolic trajectories on infinite- or finite-time intervals ⋮ Transversal homoclinic orbits for higher dimensional difference equations ⋮ The Chaotic Saddle in the Lozi Map, Autonomous and Nonautonomous Versions ⋮ TIME-VARYING PERTURBATIONS OF CHAOTIC DISCRETE SYSTEMS

Cites Work

• Transversal homoclinic points and hyperbolic sets for non-autonomous maps. I
• Chaotic solutions of systems with almost periodic forcing
• Exponential dichotomies and transversal homoclinic points
• Stable and Random Motions in Dynamical Systems
• Melnikov Transforms, Bernoulli Bundles, and Almost Periodic Perturbations
• Period Three Implies Chaos
• Differentiable dynamical systems
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