Levich Institute Seminar: Chaos and Homology

Michael Shub
Mathematics Department, City College of CUNY

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

Currently, Distinguished Professor, CCNY Math Dept. Previously Conicet, Argentina, University of Toronto, IBM Research, Queens College of CUNY, University de Paris Sud, University of California at Santa Cruz, Brandeis University,

MOST RECENT RESEARCH INTERESTS:

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