7 citations · 15 across the 13 of their papers we have counts for
15 papers
On disjointness of 3-IETs from mixing and lightly mixing systems
Przemysław Berk
In this note we show that all interval exchange transformations of three intervals (3-IETs) are spectrally disjoint from all mixing and disjoint from lightly mixing systems. Until…
Disjointness of rescalings of smooth area preserving flows on surfaces
Przemysław Berk, Corinna Ulcigrai
We consider the problem of \emph{disjointness of rescalings} , of a flow in the context of smooth flows pre…
Coexistence of two contrasting recurrence properties of certain non-integrable cocycles
Przemysław Berk, Łukasz Kotlewski
We study the recurrence properties of certain skew products over symmetric interval exchange transformations, including rotations, with cocycles of the form $f(x)=-\frac{1}{x^a}+\f…
Coboundaries of 3-IETs
Przemysław Berk, Carlos Ospina
In this note, we investigate coboundaries of interval exchange transformations of three intervals, or 3-IETs. More precisely, we study differentiable functions whose derivative is…
On the ergodicity of anti-symmetric skew products with singularities and its applications
Przemysław Berk, Krzysztof Frączek, Frank Trujillo
We introduce a novel method for proving ergodicity for skew products of interval exchange transformations (IETs) with piecewise smooth cocycles having singularities at the ends of…
Ergodic properties of infinite extension of symmetric interval exchange transformations
Przemysław Berk, Frank Trujillo, Hao Wu
We prove that skew products with the cocycle given by the function with are ergodic for every ergodic symmetric IET in the base, thus giving the full char…
Ergodicity of skew-products over typical IETs
Fernando Argentieri, Przemysław Berk, Frank Trujillo
We prove ergodicity of a class of infinite measure preserving systems, called skew-products. More precisely, we consider systems of the form \[ {T_f}:{[0, 1) \times \mathbb{R}}\to{…
Joining properties of automorphisms disjoint with all ergodic systems
Przemysław Berk, Martyna Górska, Thierry de la Rue
We study the class of automorphisms which are disjoint with all ergodic systems. We prove that the identities are the only multipliers of that is, each aut…
On the ergodicity of infinite antisymmetric extensions of symmetric IETs
Przemysław Berk, Frank Trujillo
In this article, we consider skew product extensions over symmetric interval exchange transformations with respect to the cocycle . More precisely, we…
Ergodicity of explicit logarithmic cocycles over IETs
Przemysław Berk, Frank Trujillo, Corinna Ulcigrai
We prove ergodicity in a class of skew-product extensions of interval exchange transformations given by cocycles with logarithmic singularities. This, in particular, gives explicit…
Rigidity for piece-wise smooth circle maps and certain GIETs
Przemysław Berk, Frank Trujillo
The goal of this article is to show a rigidity property of conjugacies of generalized interval exchange transformations (GIETs). More precisely, we show that if two piecewise …
Backward Rauzy-Veech algorithm and horizontal saddle connections
Przemysław Berk
The goal of this note is to study the action of the backward Rauzy-Veech algorithm on the translation surfaces with horizontal saddle connections. In particular, we prove that the…
Spectral disjointness of rescalings of some surface flows
Przemysław Berk, Adam Kanigowski
We study self-similarity problem for two classes of flows: (1) special flows over circle rotations and under roof functions with symmetric logarithmic singularities (2) special flo…
On typicality of translation flows which are disjoint with their inverse
Przemyslaw Berk, Krzysztof Fraczek, Thierry de la Rue
In this paper we prove that translation structures for which the corresponding vertical translation flows is weakly mixing and disjoint with its inverse, form a -dense set in…
On special flows over IETs that are not isomorphic to their inverses
Przemysław Berk, Krzysztof Frączek
In this paper we give a criterion for a special flow to be not isomorphic to its inverse which is a refine of a result in \cite{Fr-Ku-Le}. We apply this criterion to special flows…