Lyapunov exponents and other properties of $ N$-groups

Dmitry A. Filimonov (1) , Victor A. Kleptsyn (2)

1 MSU - Lomonosov Moscow State University
2 IRMAR - Institut de Recherche Mathématique de Rennes

We study the class of minimally acting finitely generated groups of $ C^2$-diffeomorphisms of the circle which have the property that the nonexpandable points are fixed, where the set of nonexpandable points is nonempty. It turns out that the Lyapunov expansion exponent of any such action is zero. As a consequence, we have a singularity of the stationary measure for a random dynamical system given by any probability distribution whose support is a finite set of the generating elements of the group.

Domaines: Systèmes dynamiques [math.DS]

Dmitry A. Filimonov, Victor A. Kleptsyn. Lyapunov exponents and other properties of $ N$-groups. Transactions of the Moscow Mathematical Society, 2012, 73, pp.29-36. ⟨10.1090/S0077-1554-2013-00198-3⟩. ⟨hal-01149746⟩