Chapter 8.7, Problem 2E

Interpretation Introduction

Interpretation:

For a vector field on a cylinder given by $\dot{\text{y}}\text{ = ay}$, $\dot{\text{θ}}\text{ = 1}$, an appropriate Poincare map is to be defined and the formula is to be found. The system has a periodic orbit which is to be shown. Also, its stability is to be classified for real values of $\text{a}\text{.}$

Concept Introduction:

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