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On measures and semiconjugacies for affine interval exchange transformations
P. Berk, K. Frączek, Ł. Kotlewski +1
In this article, we study affine interval exchange transformations (AIETs) which are semi-conjugated to interval exchange transformations (IETs) of hyperbolic periodic type. More p…
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…
On the uniqueness of affine IETs semi-conjugated to IETs
Frank Trujillo
We prove that for almost every irreducible interval exchange transformation and for any vector in its associated central-stable space (with respect to the Kontsevich-Zorich…
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{…
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 …