Recoding the Classic H\'enon-Devaney Map

TL;DR

This paper constructs a symbolic dynamics conjugacy for the classical Henon-Devaney map, providing a comprehensive understanding of its behavior and extending the coding to a broader class of maps with fixed discontinuities.

Contribution

It introduces a conjugacy to a subshift of finite type for the Henon-Devaney map and extends this coding to more general maps with fixed discontinuities.

Findings

Conjugacy to a subshift of finite type established

Global behavior of the map characterized

Coding extended to broader class of maps with fixed discontinuity

Abstract

In this work we are going to consider the classical H\'enon-Devaney map given by \begin{eqnarray*} f: \mathbb{R}^2\setminus \{y=0\} &\rightarrow& \mathbb{R}^2 \\ (x,y) &\mapsto& \left(x+\dfrac{1}{y}, y-\dfrac{1}{y}-x\right) \end{eqnarray*} We are going to construct conjugacy to a subshift of finite type, providing a global understanding of the map's behavior.We extend the coding to a more general class of maps that can be seen as a map in a square with a fixed discontinuity.