Abstract:
A connection between the deformation rate of a small set boundary in the phase space of a dynamical system and the metric entropy of the system was claimed (not too rigorously) in physics literature.

Rigorous results were obtained by B. Gurevich for discrete time Markov shifts and later generalized in my work for synchronized systems. Further, such a
connection was established in our joint work with B. Gurevich for Anosov diffeomorphisms, and suspension flows in joint work with B. Gurevich and A. Tempelman.
For symbolic dynamical systems we estimate the deformation rate in terms of an ergodic invariant measure, while for Anosov systems we use the volume. I will present specific details of our approach.