Hyperbolicity of the invariant sets for the real polynomial maps

Details Hyperbolicity of the invariant sets for the real polynomial maps Hyperbolicity of the invariant sets for the real polynomial maps

2010-12-22

arxiv.org/abs/1012.4997v1

Mathematics

Dynamical Systems

21 pages

Scientific paper

It is well known that for $a>4$, the dynamical behaviors of the logistic map $f_a(x)=ax(1-x)$ on the maximal invariant compact set are "simple" which could be clearly explained by the theories of hyperbolic dynamics and symbolic dynamics. Is it possible that similar phenomena could be observed in general real polynomial maps? In this paper, we study this problem by investigating the real polynomial map $f_a(x)=ag(x)$, where $a$ is a parameter, and $g$ is a real-coefficient polynomial, which has at least two different real zeros or only one real zero.

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