ABSTRACT

Algebraic topology associates some matrices to a smooth discrete dynamical system. The logs of the moduli of the eigenvalues of these matrices provide a lower bound for the entropy. As the matrices are very robust, they don’t change under homotopy of the dynamics, they give a robust, quantitative estimate of the chaos. I will discuss some history, examples and open problems. I hope that this might be interesting to physicists at least on a philosophical level.

BRIEF ACADEMIC/EMPLOYMENT HISTORY:

MOST RECENT RESEARCH INTERESTS:  

Entropy conjecture in low smoothness, smooth periodic point growth, random versus deterministic exponents in linear algebra.