EVENT DETAILS AND ABSTRACT

Title: Simplicity of the Lyapunov spectrum via Boundary theory
Speaker: Alex Furman
Speaker Info: University of Illinois, Chicago
Brief Description:
Special Note:
Abstract:

Consider products of matrices in $G=SL(d,R)$ that are chosen using some ergodic dynamical system. The Multiplicative Ergodic Theorem (Oseledets) asserts that the asymptotically such products behave as $\exp(n\Lambda)$ where $\Lambda$ is a fixed diagonal traceless matrix, called the Lyapunov spectrum of the system. The spectrum $\Lambda$ depends on the system in a mysterious way, and is almost never known explicitly. The best understood case is that of random walks, where by the work of Furstenberg, Guivarc'h-Raugi, and Gol'dsheid-Margulis we know that the spectrum is simple (i.e. all values are distinct) provided the random walk is not trapped in a proper algebraic subgroup. Recently, Avila and Viana proved a conjecture of Kontsevich-Zorich that asserts simplicity of the Lyapunov spectrum for another system related to the Teichmuller flow.