Symbolic dynamics of tree maps

Abstract

The symbolic dynamics of a class of tree maps is analysed. There are three symbolic dynamical systems associated to such a map. They can best be understood in terms of sofic systems, which are generalizations of subshifts of finite type. Several examples are provided to illustrate these ideas.

Keywords:

• tree maps
• symbolic dynamics
• topology
• sofic systems

Acknowledgements

I would like to thank Lluís Alsedà for introducing us to these tree maps and my colleagues Will Geller, Michal Misiurewicz and Rodrigo Perez for our many discussions.