On Hyperbolic Plateaus of the Henon Map

DOI10.1080/10586458.2007.10128992zbMath1145.37023OpenAlexW1973273804MaRDI QIDQ3512344

Zin Arai

Publication date: 11 July 2008

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10586458.2007.10128992

zbMATH Keywords

computer-assisted proofuniform hyperbolicity

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) General methods in interval analysis (65G40) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Dynamical systems with hyperbolic orbits and sets (37D05) Computational methods for bifurcation problems in dynamical systems (37M20)

Related Items (13)

Complexified stable and unstable manifolds and chaotic tunneling ⋮ Recent development in rigorous computational methods in dynamical systems ⋮ Using periodic orbits to compute chaotic transport rates between resonance zones ⋮ On parameter loci of the Hénon family ⋮ Uniform hyperbolicity of a class of scattering maps ⋮ Validated numerics for continuation and bifurcation of connecting orbits of maps ⋮ Semi-parabolic tools for hyperbolic Hénon maps and continuity of Julia sets in $\mathbb {C}^{2}$ ⋮ Rigorous bounds for polynomial Julia sets ⋮ On loops in the hyperbolic locus of the complex Hénon map and their monodromies ⋮ Finite resolution dynamics ⋮ s-limit shadowing is \(\mathcal C^0\)-dense ⋮ Parallelization method for a continuous property ⋮ On Topological Entropy of Finite Representations of the Hénon Map

Uses Software

• SaddleDrop

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