On hyperbolic plateaus of the Hénon map. (English) Zbl 1145.37023

Arai, Zin

Exp. Math. 16, No. 2, 181-188 (2007).

Summary: We propose a rigorous computational method to prove the uniform hyperbolicity of discrete dynamical systems. Applying the method to the real Hénon family, we prove the existence of many regions of hyperbolic parameters in the parameter plane of the family.

MSC:

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

Keywords:

uniform hyperbolicity; computer-assisted proof

Software:

SaddleDrop