65 citations · 277 across the 54 of their papers we have counts for
31 papers · 1 filter
Irrational rotation dynamics for unimodal maps
Konstantin Bogdanov, Alexander Bufetov
The first result of the paper (Theorem 1.1) is an explicit construction of unimodal maps that are semiconjugate, on the post-critical set, to the circle rotation by an arbitrary ir…
Self-similarity and spectral theory: on the spectrum of substitutions
Alexander I. Bufetov, Boris Solomyak
In this survey of the spectral properties of substitution dynamical systems we consider primitive aperiodic substitutions and associated dynamical systems: -actions an…
On substitution automorphisms with pure singular spectrum
Alexander I. Bufetov, Boris Solomyak
A sufficient condition for a substitution automorphism to have pure singular spectrum is given in terms of the top Lyapunov exponent of the associated spectral cocycle. As a coroll…
Hölder regularity for the spectrum of translation flows
Alexander I. Bufetov, Boris Solomyak
The paper is devoted to generic translation flows corresponding to Abelian differentials on flat surfaces of arbitrary genus . These flows are weakly mixing by the Avila-Fo…
Convergence of spherical averages for actions of Fuchsian Groups
Alexander I. Bufetov, Alexey Klimenko, Caroline Series
Pointwise convergence of spherical averages is proved for a measure-preserving action of a Fuchsian group. The proof is based on a new variant of the Bowen-Series symbolic coding f…
A spectral cocycle for substitution systems and translation flows
Alexander I. Bufetov, Boris Solomyak
For substitution systems and translation flows, a new cocycle, which we call {\em spectral cocycle}, is introduced, whose Lyapunov exponents govern the local dimension of the spect…