From the 1 of 8 linked papers with an AI index.
8 papers
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…
Generalized Aubry-André formula and continuity of the intersection spectrum of the Almost Mathieu operator
Anton Gorodetski, Victor Kleptsyn
We consider the spectrum of the Almost Mathieu operator (AMO) and show that the moments of the restriction of the Lebesgue measure to the intersection spectrum $\text{Leb}|_{Σ_{α…
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…
Central Limit Theorem for non-stationary random products of $\SL(2, \R)$ matrices
Anton Gorodetski, Victor Kleptsyn, Grigorii Monakov
We prove Central Limit Theorem for non-stationary random products of matrices, generalizing the classical results by Le Page and Tutubalin that were obtained in…
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…