Chapter 12.2, Problem 4E

Interpretation Introduction

Interpretation:

To find all the fixed points of the Henon mapand to show that they exist only if ${\text{a > a}}_{\text{0}}$, where ${\text{a}}_{\text{0}}$ is to be determined.

Concept Introduction:

• The Henon map is represented by the following system of equations: ${\text{x}}_{\text{n+1}}{\text{ = 1 + y}}_{\text{n}}{\text{ - ax}}_{\text{n}}^{\text{2}}$ and ${\text{y}}_{\text{n+1}}{\text{ = bx}}_{\text{n}}$.

• The second equation of the Henon map can be written as:-

  $\begin{array}{l}{\text{y}}_{\text{n+1}}{\text{ = bx}}_{\text{n}}\\ {\text{y}}_{\text{n}}{\text{ = bx}}_{\text{n-1}}\end{array}$