Numerical approximation of homoclinic chaos

DOI10.1023/A:1019196426363zbMath0898.65041OpenAlexW1976107721MaRDI QIDQ1370346

J.-M. Kleinkauf, Wolf-Jürgen Beyn

Publication date: 8 November 1998

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1019196426363

zbMATH Keywords

chaosNewton's methoddynamical systemsBernoulli shifthomoclinic pointsSmale's theoremtransversal homoclinic orbitshomoclinic symbol sequence

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Dynamical systems with hyperbolic behavior (37D99)

Related Items (10)

Angular Values of Nonautonomous Linear Dynamical Systems: Part II – Reduction Theory and Algorithm ⋮ Quadratic volume-preserving maps: (Un)stable manifolds, hyperbolic dynamics, and vortex-bubble bifurcations ⋮ Validated numerics for continuation and bifurcation of connecting orbits of maps ⋮ Computer assisted error bounds for linear approximation of (un)stable manifolds and rigorous validation of higher dimensional transverse connecting orbits ⋮ Polynomial approximation of one parameter families of (un)stable manifolds with rigorous computer assisted error bounds ⋮ COMPUTING INVARIANT SETS ⋮ Error estimates for approximating non-hyperbolic heteroclinic orbits of maps ⋮ A Contour Algorithm for Computing Stable Fiber Bundles of Nonautonomous, Noninvertible Maps ⋮ Homoclinic shadowing ⋮ Chaotic behaviour near non-transversal homoclinic points with quadratic tangency

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