Accessible saddles on fractal basin boundaries

DOI10.1017/S0143385700006842zbMath0767.58023OpenAlexW2087126825MaRDI QIDQ4015514

James A. Yorke, Kathleen T. Alligood

Publication date: 18 January 1993

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0143385700006842

zbMATH Keywords

rotation numberboundary behaviourprime endsRiemann mapping theorem

Mathematics Subject Classification ID

Topological dynamics (37B99) Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Dynamical systems with hyperbolic behavior (37D99) Cluster sets, prime ends, boundary behavior (30D40)

Related Items (22)

Attractors with irrational rotation number ⋮ Rotational chaos in dissipative systems ⋮ Bifurcations of basins of attraction from the view point of prime ends ⋮ Wada basin boundaries and basin cells ⋮ Homotopically unbounded disks for generic surface diffeomorphisms ⋮ Parametrized family of pseudo‐arc attractors: Physical measures and prime end rotations ⋮ WADA FRACTAL BASINS OF ATTRACTION IN A ZERO-STIFFNESS VIBRATION ISOLATION SYSTEM ⋮ A really topological treatment of some aspects of Carathéodory’s theory of prime ends ⋮ Switching-induced Wada basin boundaries in the Hénon map ⋮ Attractors with vanishing rotation number ⋮ Strange nonchaotic attractors with Wada basins ⋮ Periodicity and Decomposability of Basin Boundaries with Irrational Maps on Prime Ends ⋮ A fixed point theorem for plane separating continua ⋮ The graph of the logistic map is a tower ⋮ Natural extensions of unimodal maps: virtual sphere homeomorphisms and prime ends of basin boundaries ⋮ Wada basin boundaries in switched systems ⋮ Selection rules for periodic orbits and scaling laws for a driven damped quartic oscillator ⋮ Accessible points rotate as prime ends in backward or forward time ⋮ Prime ends rotation numbers and periodic points ⋮ Rate of escape from nonattracting chaotic sets. ⋮ A procedure for finding numerical trajectories on chaotic saddles ⋮ Rotation numbers of periodic orbits in the Hénon map

Cites Work

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• Area preserving twist homeomorphism of the annulus
• Rotation numbers of periodic orbits in the Hénon map
• Metamorphoses: Sudden jumps in basin boundaries

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