An upper bound on the dimension of the Rauzy gasket

Pollicott, Mark; Sewell, Benedict

doi:10.48550/arxiv.2110.07264

2021

DOI: 10.48550/arxiv.2110.07264

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An upper bound on the dimension of the Rauzy gasket

Mark Pollicott¹,

Benedict Sewell²

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“…Remark 8. Subsequently, our result has been updated several times: first, by Fougeron [35] and then by Policott and Sewell [59], whose upper bound of 1.74 is the sharpest so far. This estimate matches well with the results of numerical experiment in [22].…”

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Renormalization in one-dimensional dynamics

Skripchenko

2023

Russian Math. Surveys

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The study of the dynamical and topological properties of interval exchange transformations and their natural generalizations is an important problem, which lies at the intersection of several branches of mathematics, including dynamical systems, low-dimensional topology, algebraic geometry, number theory, and geometric group theory. The purpose of the survey is to make a systematic presentation of the existing results on the ergodic and geometric characteristics of the one-dimensional maps under consideration, as well as on the measured foliations on surfaces and two-dimensional complexes that one can associate with these maps. These results are based on the research of the ergodic properties of the renormalization process - an algorithm that takes an original dynamical system and builds a sequence of equivalent dynamical systems with a smaller support set. For all dynamical systems considered in the paper these renormalization algorithms can be viewed as multidimensional fraction algorithms. Bibiliography: 74 titles.

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Renormalization in one-dimensional dynamics

Skripchenko

2023

Russian Math. Surveys

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An upper bound on the dimension of the Rauzy gasket

Cited by 1 publication

References 10 publications

Renormalization in one-dimensional dynamics

Renormalization in one-dimensional dynamics

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