Isolating segments, fixed point index, and symbolic dynamics. III: Applications

DOI10.1006/jdeq.2001.4099zbMath1025.37013OpenAlexW2017397818MaRDI QIDQ697869

Piotr Zgliczyński, Klaudiusz Wójcik

Publication date: 17 September 2002

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

Full work available at URL: https://doi.org/10.1006/jdeq.2001.4099

zbMATH Keywords

Poincaré mapnonautonomous equationchaotic properties

Mathematics Subject Classification ID

Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Complex behavior and chaotic systems of ordinary differential equations (34C28) Symbolic dynamics (37B10) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

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Relative Nielsen numbers, braids and periodic segments ⋮ Entropy for symbolic dynamics with overlapping alphabets ⋮ Fixed points of the area preserving Poincaré maps on two-manifolds ⋮ Strong pairs of periodic segments ⋮ Periodic points of the planar area preserving Poincaré map inside isolating segment ⋮ Symbolic dynamics for nonhyperbolic systems ⋮ Remark on complicated dynamics of some planar system

Cites Work

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• A geometric method for detecting chaotic dynamics
• Fixed point index for iterations of maps, topological horseshoe and chaos
• Isolating segments, fixed point index, and symbolic dynamics
• Computer assisted proof of chaos in the Rössler equations and in the Hénon map
• Periodic and bounded solutions in blocks for time-periodic nonautonomous ordinary differential equations
• ON SOME NONAUTONOMOUS CHAOTIC SYSTEM ON THE PLANE
• Isolating segments, fixed point index, and symbolic dynamics. II: Homoclinic solutions
• On detecting periodic solutions and chaos in the time periodically forced ODEs

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