SMS scnews item created by Lachlan Smith at Fri 5 Jun 2020 1720
Type: Seminar
Distribution: World
Expiry: 31 Jul 2020
Calendar1: 12 Jun 2020 1700-1800
CalLoc1: Zoom
CalTitle1: Sydney Dynamics Group: Reza Mohammadpour -- Lyapunov spectrum properties
Auth: lachlans@105.66.233.220.static.exetel.com.au (lsmi9789) in SMS-WASM

# Sydney Dynamics Group: Mohammadpour -- Lyapunov spectrum properties

Dear all,

Next week, Friday June 12, Reza Mohammadpour (IMPAN-Warsaw) will give a talk at 5pm
(Sydney time) via Zoom.  Note the unusual time.
Meeting ID: 978 8117 7562

Title: Lyapunov spectrum properties

Abstract:
In this talk we discuss ergodic optimization and multifractal behaviour of Lyapunov
exponents for matrix cocycles.  We show that the restricted variational principle holds
for generic cocycles over mixing subshifts of finite type, and the Lyapunov spectrum is
equal to the closure of the set where the entropy spectrum is positive for such
cocycles.  Moreover, we show both the continuity of the entropy spectrum at the boundary
of Lyapunov spectrum for such cocycles, and the continuity of the lower joint spectral
radius for linear cocycles under the assumption that linear cocycles satisfy a cone
condition.  We consider a subadditive potential $\Phi$.  We obtain that for
$t\rightarrow \infty$ any accumulation point of a family of equilibrium states of
$t\Phi$ is a maximizing measure, and that the Lyapunov exponent and entropy of
equilibrium states for $t\Phi$ converge in the limit $t\rightarrow \infty$ to the
maximum Lyapunov exponent and entropy of maximizing measures.

Past talks can be found on the YouTube channel: