Chapter 12.2, Problem 3E

Interpretation Introduction

Interpretation:

Toredraw Figure $\mathrm{12.2.1}$, using an ellipse instead of a rectangle as the test shape. To sketch the successive images of the ellipse under the maps ${\text{T}}^{\prime }\text{, }{\text{T}}^{″}\text{, }{\text{T}}^{‴}$. To represent the ellipse parametrically, and to draw accurate plots on a computer.

Concept Introduction:

Hénon map is given by

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

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