¾«¶«Ó°Òµ

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, ¾«¶«Ó°Òµ 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.