Spatial limit theorem for interval exchange transformations

zbMATH Open1460.37038arXiv1901.05570MaRDI QIDQ5112486

Alexey Klimenko

Publication date: 29 May 2020

Abstract: We prove a spatial limit theorem for generic interval exchange transformations (IETs): for a generic IET the normalized ergodic sums of a sufficiently regular (e.g., Lipschitz) function have the same asymptotic behavior of distributions as the behaviour of ergodic integrals for a generic translation flow on a flat surface, described by A. Bufetov.

Full work available at URL: https://arxiv.org/abs/1901.05570

zbMATH Keywords

limit theoremfinitely additive measuresBufetov cocyclesinterval exchanger transformation

Mathematics Subject Classification ID

Ergodic theorems, spectral theory, Markov operators (37A30) Dynamical systems involving maps of the interval (37E05) Flows on surfaces (37E35)

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