Arnold's cat map

(Prof. Dr. Anke Pohl)

Arnold's cat mapping is the self-mapping of the 2-torus $\mathbb{R}^2/\mathbb{Z}^2$ given by $\ F(x,y)\equiv(2x+y, x+y)\; \mod 1$. If one draws the image of a cat on the 2-torus, discretizes it and applies the mapping F iterated, the cat becomes unrecognizable at first. After finitely many steps, however, one gets back the original image of the cat. The goal of this project is to find an image of a cat for which an image of a dog is generated at least once during the iteration.

Basic knowledge of calculus and linear algebra is recommended. The duration of the work within the working group should be at least four weeks. In addition, a written paper and a final presentation in the seminar are expected. Further information and requirements can be found in the module and event catalog of the Department of Mathematics.

A written presentation of this topic can be found here.