Abstract

Consider a real-analytic function $f$ on a Euclidean space, and suppose $f(0)=0$. The Lojasiewicz gradient inequality asserts the existence of a positive exponent , such that $|f(x)|a/|f\prime (x)|$ is bounded above near $0$. This is a crucial tool for the recent proof of the famous "gradient conjecture of R. Thom", that speepest descent trajectories for real-analytic functions do not oscillate near critical points. In this talk, we shall outline some nonsmooth variants, and discuss applications to subgradient dynamical systems.

This is a joint work with Jerome Bolte (Universidad de Santiago, Chile) and Adrian Lewis (Simon Fraser University, Canada)