NUMERICAL STUDY OF COEXISTING ATTRACTORS FOR THE HÉNON MAP

DOI10.1142/S0218127413300255zbMath1275.37023OpenAlexW2115371521MaRDI QIDQ2864933

Zbigniew Galias, Warwick Tucker

Publication date: 27 November 2013

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127413300255

zbMATH Keywords

interval arithmeticperiodic orbitHénon mapcoexisting attractors

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Approximation methods and numerical treatment of dynamical systems (37M99)

Related Items (9)

On computer-assisted proving the existence of periodic and bounded orbits ⋮ A database of rigorous and high-precision periodic orbits of the Lorenz model ⋮ On the structure of existence regions for sinks of the Hénon map ⋮ Is the Hénon attractor chaotic? ⋮ How to Bridge Attractors and Repellors ⋮ Transition-based complexity-entropy causality diagram: a novel method to characterize complex systems ⋮ Coexistence of Strange Nonchaotic Attractors in a Quasiperiodically Forced Dynamical Map ⋮ Existence of Periodic Solutions of the FitzHugh--Nagumo Equations for an Explicit Range of the Small Parameter ⋮ A Four-Leaf Chaotic Attractor of a Three-Dimensional Dynamical System

Cites Work

• The dynamics of the Hénon map
• A two-dimensional mapping with a strange attractor
• The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
• VALIDATED STUDY OF THE EXISTENCE OF SHORT CYCLES FOR CHAOTIC SYSTEMS USING SYMBOLIC DYNAMICS AND INTERVAL TOOLS
• COUNTING LOW-PERIOD CYCLES FOR FLOWS
• Simplicial and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations
• Bifurcation structures in maps of Hénon type
• CALCULATING STABLE AND UNSTABLE MANIFOLDS
• ON THE MENDÈS FRANCE FRACTAL DIMENSION OF STRANGE ATTRACTORS: THE HÉNON CASE
• INTERVAL METHODS FOR RIGOROUS INVESTIGATIONS OF PERIODIC ORBITS

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