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