Hyperbolic sets, transversal homoclinic trajectories, and symbolic dynamics for \(C^ 1\)-maps in Banach spaces

DOI10.1007/BF01048949zbMath0702.58051OpenAlexW2083533842MaRDI QIDQ915229

Hans-Otto Walther, Heinrich Steinlein

Publication date: 1990

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01048949

zbMATH Keywords

symbolic dynamicshyperbolic setgeneralized hyperbolic structurestransversal homoclinic trajectories

Mathematics Subject Classification ID

Low-dimensional dynamical systems (37E99) Dynamical systems with hyperbolic behavior (37D99)

Related Items (15)

Recent results on the topological fixed point theory of multivalued mappings: a survey ⋮ Persistence of Poincaré mappings in functional differential equations (with application to structural stability of complicated behavior) ⋮ Floquet multipliers and secondary bifurcations in functional differential equations: Numerical and analytical results ⋮ Generalized hyperbolic sets on Banach spaces ⋮ Chaotic learning equilibria ⋮ Semi-unimodal 2-endomorphisms with complicated nonwandering set ⋮ Shadowing and Silnikov chaos ⋮ On areas of attraction and repulsion in finite time dynamical systems and their numerical approximation ⋮ NUMERICAL ANALYSIS OF DEGENERATE CONNECTING ORBITS FOR MAPS ⋮ Error estimates for approximating non-hyperbolic heteroclinic orbits of maps ⋮ A shadowing theorem for ordinary differential equations ⋮ A simple proof for persistence of snap-back repellers ⋮ A delay differential equation with a solution whose shortened segments are dense ⋮ Erratic solutions of simple delay equations ⋮ Parameterized stable/unstable manifolds for periodic solutions of implicitly defined dynamical systems

Cites Work

• Symbolic dynamics and nonlinear semiflows
• Transversal homoclinic points and hyperbolic sets for non-autonomous maps. I
• Snap-back repellers imply chaos in \(\mathbb{R}^n\)
• Chaotic Behaviour in Simple Dynamical Systems
• A Shadowing Lemma with Applications to Semilinear Parabolic Equations
• Transverse homoclinic orbits in periodically perturbed parabolic equations
• Examples of transverse homoclinic orbits in delay equations
• Homoclinic solution and chaos in
• Hyperbolic periodic solutions, heteroclinic connections and transversal homoclinic points in autonomous differential delay equations
• Differentiable dynamical systems
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