Local rigidity for periodic generalised interval exchange transformations
Sign Up to like & getrecommendations! Published in 2019 at "Inventiones mathematicae"
DOI: 10.1007/s00222-021-01051-3
Abstract: In this article we study local rigidity properties of generalised interval exchange maps using renormalisation methods. We study the dynamics of the renormalisation operator $\mathcal{R}$ acting on the space of $\mathcal{C}^{3}$-generalised interval exchange transformations at… read more here.
Keywords: exchange; exchange transformations; interval exchange; local rigidity ... See more keywords
The set of uniquely ergodic interval exchange transformations is path-connected
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DOI: 10.1017/etds.2017.34
Abstract: Let $\unicode[STIX]{x1D70B}$ be a non-degenerate permutation on at least four symbols. We show that the set of uniquely ergodic interval exchange transformations with permutation $\unicode[STIX]{x1D70B}$ is path-connected. read more here.
Keywords: uniquely ergodic; interval exchange; ergodic interval; set uniquely ... See more keywords
Cutting and shuffling with diffusion: Evidence for cut-offs in interval exchange maps.
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DOI: 10.1103/physreve.98.022221
Abstract: Low-dimensional dynamical systems are fruitful models for mixing in fluid and granular flows. We study a one-dimensional discontinuous dynamical system (termed "cutting and shuffling" of a line segment), and we present a comprehensive computational study… read more here.
Keywords: diffusion; interval exchange; number; cutting shuffling ... See more keywords
Non-injectivity of infinite interval exchange transformations and generalized Thue-Morse sequences
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DOI: 10.3934/dcds.2023048
Abstract: In this paper we study the non-injectivity arising in infinite interval exchange transformations. In particular, we build and analyze an infinite family of infinite interval exchanges semi-conjugated to generalized Thue-Morse subshifts, whose non-injectivity occurs at… read more here.
Keywords: exchange transformations; non injectivity; interval exchange; generalized thue ... See more keywords