Shilnikov's cross-map method and hyperbolic dynamics of three-dimensional Hénon-like maps

DOI10.1134/S1560354710020061zbMath1203.37029OpenAlexW1991326063MaRDI QIDQ618193

Ming-Chia Li, Sergey V. Gonchenko

Publication date: 14 January 2011

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1560354710020061

zbMATH Keywords

symbolic dynamicssaddlehyperbolic setSmale horseshoequadratic mapsaddlefocus

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Symbolic dynamics (37B10) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Related Items (4)

Invariant manifolds of homoclinic orbits and the dynamical consequences of a super-homoclinic: a case study in \(\mathbb{R}^4\) with \(\mathbb{Z}_2\)-symmetry and integral of motion ⋮ Scenarios for the creation of hyperchaotic attractors in 3D maps ⋮ Criteria on existence of horseshoes near homoclinic tangencies of arbitrary orders ⋮ Shilnikov attractors in three-dimensional orientation-reversing maps

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