Markov partitions, Martingale and symmetric conjugacy of circle endomorphisms

Hu, Yunchun

doi:10.1090/proc/13400

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2021

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“…That is, the conjugacy between two geometrically finite onedimensional maps is smooth if and only if the maps have the same scaling function and the exponents of the corresponding power-law singularities are the same. More results on differential properties and the symmetric properties of a conjugacy between two one-dimensional maps are given in [6,17]. Finally, the symmetric regularity of the conjugacy between two one-dimensional maps (with possible singularities) becomes an important issue in the study of one-dimensional dynamical systems, in particular in the study of geometric Gibbs theory (see [11,15,16]).…”

Section: Introductionmentioning

confidence: 99%

Symmetric Rigidity for Circle Endomorphisms with Bounded Geometry

Adamski,

Hu,

Jiang

et al. 2021

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Let f and g be two circle endomorphisms of degree d ≥ 2 such that each has bounded geometry, preserves the Lebesgue measure, and fixes 1. Let h fixing 1 be the topological conjugacy from f to g. That is, h • f = g • h. We prove that h is a symmetric circle homeomorphism if and only if h = Id. Many other rigidity results in circle dynamics follow from this very general symmetric rigidity result.

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Section: Introductionmentioning

confidence: 99%