Chapter 12.1, Problem 7E

Interpretation Introduction

Interpretation:

Find the points in the original square that map to the square at the lower left of the Smale horseshoe figure given in the problem. To show that after the next round of the mapping, the square on the lower left contains four horizontal strips. To find where they came from in the original square. To describe the set of points in the original square that surviveforever.

Concept Introduction:

• In the Smale horseshoe map, the horseshoe hangs over the edge of the original square. The overhanging parts are lopped off before the next iteration proceeds.

• The Smale horseshoe map does not have a strange attractor.