 
Summary: On Hyperbolic Plateaus of the H´enon Map
Zin ARAI
Department of Mathematics, Kyoto University, Kyoto 6068502, Japan
(email: arai@math.kyotou.ac.jp)
Abstract
We propose a rigorous computational method to prove the uniform
hyperbolicity of discrete dynamical systems. Applying the method
to the real H´enon family, we prove the existence of many regions of
hyperbolic parameters in the parameter plane of the family.
1 Introduction
Consider the problem of determining the set of parameter values for which
the real H´enon map
Ha,b : R2
R2
: (x, y) (a  x2
+ by, x) (a, b R)
is uniformly hyperbolic. If a dynamical system is uniformly hyperbolic, gen
erally speaking, we can apply the socalled hyperbolic theory of dynamical
systems and obtain many results on the behavior of the system. Despite its
importance, however, proving hyperbolicity is a difficult problem even for
