From the 1 of 8 linked papers with an AI index.
5 papers · 1 filter
Atomic physical measures for non-invertible random dynamical systems
Vincent P. H. Goverse, Victor Kleptsyn
The authors construct a random dynamical system on the circle, using locally invertible maps, that has an atomic stationary measure which is physical—typical random orbits converge…
Critical regularity of nilpotent groups acting on one-dimensional compact manifolds
Maximiliano Escayola, Victor Kleptsyn
Given a finitely generated, torsion-free nilpotent group, we find the maximum possible (critical) regularity for its faithful actions by diffeomorphisms of the closed or half-open…
The fibered rotation number
Pedro Duarte, Anton Gorodetski, Victor Kleptsyn
We provide an explicit formula for an increment of the fibered rotation number of a one-parameter family of circle cocycles over any ergodic transformation in terms of invariant me…
On the Regularity of the Dimension of Cookie-Cutter-Like Sets
Victor Kleptsyn, Alexandro Luna
We study the Hausdorff and box-counting dimensions of cookie-cutter-like sets formed by sequential dynamics of a finite number of expanding maps. Under some natural conditions, the…
Log Hölder continuity of the rotation number
Anton Gorodetski, Victor Kleptsyn
We consider one-parameter families of smooth circle cocycles over an ergodic transformation in the base, and show that their rotation numbers must be log-Hölder regular with respe…