6 papers · 1 filter
Coboundaries of 3-IETs
PrzemysÅaw 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…
Disjointness of rescalings of smooth area preserving flows on surfaces
PrzemysÅaw Berk, Corinna Ulcigrai
We consider the problem of \emph{disjointness of rescalings} , of a flow in the context of smooth flows…
Coexistence of two contrasting recurrence properties of certain non-integrable cocycles
PrzemysÅaw Berk, Åukasz 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…
On the ergodicity of anti-symmetric skew products with singularities and its applications
PrzemysÅaw Berk, Krzysztof FrÄ czek, 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
PrzemysÅaw 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, PrzemysÅaw 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{…