A note on the hyperbolicity of the non-wandering sets of real quadratic maps

Diyath Pannipitiya

paper

A note on the hyperbolicity of the non-wandering sets of real quadratic maps

arXiv:2402.05433

Abstract

The goal of this paper is to discuss about the hyperbolicity of the non-wandering set $NW (f_{c})$ of real quadratic function $f_{c} (x) = x^{2} + c$ when $c \in (- \infty, - 2]$ . Even though the results we present here are not new, it is not easier to find the proofs of them. We present two different ways to prove the hyperbolicity of $NW (f_{c})$ for the``considerably difficult case'' of when $c$ is closer to $- 2$ .