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

DOI10.1007/BF00948961zbMath0672.58034OpenAlexW2008846506MaRDI QIDQ1120171

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/bf00948961

zbMATH Keywords

Melnikov methodhyperbolic setshomoclinic points

Mathematics Subject Classification ID

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

Related Items

Transversal Bounded Solutions for Difference Equations ⋮ Invariant manifold templates for chaotic advection ⋮ Variable steps for reversible integration methods ⋮ Chaotic Dynamics in Nonautonomous Maps: Application to the Nonautonomous Hénon Map ⋮ Canonical Runge-Kutta methods ⋮ Computation of stable and unstable manifolds of hyperbolic trajectories in two-dimensional, aperiodically time-dependent vector fields ⋮ On the position of chaotic trajectories ⋮ Conservation of invariants by symmetric multistep cosine methods for second-order partial differential equations ⋮ Chaos in almost periodic systems ⋮ Hyperbolic sets, transversal homoclinic trajectories, and symbolic dynamics for \(C^ 1\)-maps in Banach spaces ⋮ On the chaotic behaviour of discontinuous systems ⋮ Invariant manifolds and control of hyperbolic trajectories on infinite- or finite-time intervals ⋮ Bifurcation and chaos near sliding homoclinics ⋮ The Chaotic Saddle in the Lozi Map, Autonomous and Nonautonomous Versions ⋮ An example of chaotic behaviour in presence of a sliding homoclinic orbit ⋮ On energy conservation of the simplified Takahashi-Imada method ⋮ Transversal homoclinic points and hyperbolic sets for non-autonomous maps. II ⋮ A shadowing theorem for ordinary differential equations ⋮ Symplectic phase flow approximation for the numerical integration of canonical systems ⋮ CHAOS IN NONAUTONOMOUS DIFFERENTIAL INCLUSIONS ⋮ TIME-VARYING PERTURBATIONS OF CHAOTIC DISCRETE SYSTEMS

Cites Work

• Transversal homoclinic points and hyperbolic sets for non-autonomous maps. II
• Chaotic solutions of systems with almost periodic forcing
• Exponential dichotomies and transversal homoclinic points
• Stable and Random Motions in Dynamical Systems
• Period Three Implies Chaos
• Differentiable dynamical systems
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item