Chapter 8.7, Problem 9E

Interpretation Introduction

Interpretation:

A Poincare map is to be computed from $\text{S}$ to itself for a system ${\dot{\text{r}}\text{ = r - r}}^{\text{2}}\text{, }\dot{\text{θ}}\text{ = 1}$. Its stability is to be classified as well. Also, the system has a unique periodic orbit which is to be shown and a multiplier of this periodic orbit is to be found.

Concept Introduction:

Poincare map is defined by ${\text{x}}_{\text{k+1}}\text{ = P}\left({\text{x}}_{\text{k}}\right)$.