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arXiv · 1801.00204

Filled Julia set of some class of H\'enon-like map

Danilo Antonio Caprio
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Abstract

In this work we consider a class of endomorphisms of $\mathbb{R}^2$ defined by $f(x,y)=(xy+c,x)$, where $c\in\mathbb{R}$ is a real number and we prove that when $-1<c<0$, the forward filled Julia set of $f$ is the union of stable manifolds of fixed and $3-$periodic points of $f$. We also prove that the backward filled Julia set of $f$ is the union of unstable manifolds of the saddle fixed and $3-$periodic points of $f$.

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Danilo Antonio Caprio. 2017-12-30. Filled Julia set of some class of H\'enon-like map. https://arxiv.org/abs/1801.00204

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