Chapter 12.2, Problem 16E

Interpretation Introduction

Interpretation:

To find and classify the fixed points of the Lozi map.

Concept Introduction:

• 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.

• A Lozi map is a two $\text{-}$ dimensional map. It is similar to the Henon map but with the term ${\text{-ax}}_{\text{n}}^{\text{2}}$ replaced by $\text{-a}\left|{\text{x}}_{\text{n}}\right|$.