Chapter 12.2, Problem 10E

Interpretation Introduction

Interpretation:

The orbit of the Hénon map which escapes to infinity is to be found.

Concept Introduction:

Hénon map is given by

${\text{x}}_{\text{n + 1}}{\text{ = y}}_{\text{n}}{\text{ + 1 - ax}}_{\text{n}}{}^{\text{2}}$

${\text{y}}_{\text{n + 1}}{\text{ = bx}}_{\text{n}}$

where $\text{a,b}$ are adjustable parameters.

Properties of Hénon map:

It is invertible.

It is dissipative.

It has a trapping region for certain parameter values.

Some orbits of the Hénon map escape to infinity.