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arXiv · 2210.16343

Ergodicity of explicit logarithmic cocycles over IETs

Przemysław Berk·Frank Trujillo·Corinna Ulcigrai
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Abstract

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 examples of ergodic $\mathbb{R}$-extensions of minimal locally Hamiltonian flows with non-degenerate saddles in genus two. More generally, given any symmetric irreducible permutation, we show that for almost every choice of lengths vector, the skew-product built over the IET with the given permutation and lengths vector given by a cocycle, with symmetric, logarithmic singularities, which is \emph{odd} when restricted to each continuity subinterval is ergodic.

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Przemysław Berk, Frank Trujillo, Corinna Ulcigrai. 2023-08-04. Ergodicity of explicit logarithmic cocycles over IETs. https://arxiv.org/abs/2210.16343

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