The Avalanche Principle and Negative Curvature

ABSTRACT:

In 2001, M. Goldstein and W. Schlag introduced the Avalanche Principle, a quantitative sufficient condition for the operator norm  $\|A_N\cdots A_1\|$ of a product of matrices in $\mathrm{SL}_2(\mathbb{R})$, to being similar to the product $\|AN\|\cdots \|A_1\|$. Since then several refinements and generalizations have  appeared in the literature.  In this talk I will present a reformulation of this principle in terms of the geometry of the hyperbolic plane, and show how to extend it to metric spaces of negative curvature.

Posted on Jun 27, 2019 in Dynamical Systems, Seminars