Chapter 12.2, Problem 1E

Interpretation Introduction

Interpretation:

To show that the product mapping -$\text{T’’’ T’’ T’}$ isequivalent to the formulas -${\text{x}}_{\text{n+1}}{\text{= y}}_{\text{n}}{\text{+1- ax}}_{\text{n}}^{\text{2}}{\text{, y}}_{\text{n+1}}{\text{= bx}}_{\text{n}}$

Concept Introduction:

• The Henon map is a two-dimensional map witha strange attractor. It captures the essential features of the Lorenz system but also has an adjustable amount ofdissipation.

• A map is the difference equation which follows ${\text{x}}_{\text{n+1}}{\text{= f(x}}_{\text{n}}\text{)}$.

• Computationally, maps are beneficial over differential equations, as maps are faster to simulate, and their solutions can be followed more accurately for longer times.