On Hyperbolic Plateaus of the Hénon Map

Abstract

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.

Keywords:

• Primary 37D05
• Secondary 37E30, 37M20
• Hénon map
• uniform hyperbolicity
• computer-assisted proof