On the appearance order of homoclinic and heteroclinic intersections in a family of dissipative maps of the plane

DOI10.1016/S0960-0779(97)00162-8zbMath0936.37033MaRDI QIDQ1809631

Kiyotaka Tanikawa, Yoshihiro Yamaguchi

Publication date: 22 May 2000

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

zbMATH Keywords

saddlehorseshoeshomoclinic tangenciesorientation-preserving diffeomorphismshyperbolic saddleshomoclinic intersectionssaddles and may be a sink

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30)

Related Items (2)

Torus destruction via global bifurcations in a piecewise-smooth, continuous map with square-root nonlinearity ⋮ The density of the transversal homoclinic points in the Hénon-like strange attractors

Cites Work

• Unnamed Item
• The dynamics of the Hénon map
• Hyperbolicity and the creation of homoclinic orbits
• The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
• Periodic points and rotation numbers for area preserving diffeomorphisms of the plane
• On the first tangency of stable and unstable manifolds in C r planar diffeomorphisms
• Coexistence of symmetric periodic points in the standard map
• Stable and unstable manifolds in a zone of instability. II
• Crises, sudden changes in chaotic attractors, and transient chaos

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