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On Hyperbolic Plateaus of the Henon Map Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan
 

Summary: On Hyperbolic Plateaus of the H´enon Map
Zin ARAI
Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan
(email: arai@math.kyoto-u.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 so-called 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

  

Source: Arai, Zin - Department of Mathematics, Kyoto University

 

Collections: Mathematics