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math.DS2026
Atomic physical measures for non-invertible random dynamical systems
Vincent P. H. Goverse, Victor Kleptsyn
We construct an example of a random dynamical system on the circle, formed by maps that are only locally invertible, which possesses an atomic stationary measure . Moreover, thi…
math.SP2026
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,λ…
math.DS2026
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…