Chapter 12.1, Problem 3E

Interpretation Introduction

Interpretation:

To sketch the face of following figure after one more iteration of the baker’s map

Concept Introduction:

• The transformation is done following procedure

  1. The square is flattened into a $2\times a$ rectangle

  2. The rectangle is cut in half, gives two $1\times a$ rectangles.

  3. The right half is stacked on top of the left half such that its base is at the level $y=\frac{1}{2}$.

• The mathematical formulation for the square is

  $\left(x_{n+1},y_{n+1}\right)=\{\begin{array}{c}\left({\text{2x}}_{\text{n}}{\text{,ay}}_{\text{n}}\right)\text{ for 0}\le {\text{x}}_n\le \frac{1}{2}\\ \left(2x_n-1,a{y}_n+\frac{1}{2}\right)\text{ for }\frac{1}{2}\le {\text{x}}_n\le 1\end{array}$