CONDUCTANCE AND MIXING TIME IN DISCRETE DYNAMICAL SYSTEMS

Abstract

We have introduced the notion of conductance in discrete dynamical systems using the known results from graph theory applied to systems arising from the iteration of continuous functions. The conductance allowed differentiating several systems with the same topological entropy, characterizing them from the point of view of the ability of the system to go out from a small subset of the state space. There are several other definitions of conductance and the results differ from one to another. Our goal is to understand the meaning of each one concerning the dynamical behaviour in connection with the decay of correlations and mixing time. Our results are supported by computational techniques using symbolic dynamics, and the tree-structure of the unimodal and bimodal maps.