Deviations in the Franks–Misiurewicz conjecture

Passeggi, Alejandro; Sambarino, Martı́n

doi:10.1017/etds.2019.8

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Cited by 3 publications

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“…By Passeggi and Sambarino [30], any homeomorphism whose rotation set is a nontrivial segment of rational slope not passing by a rational point, has unbounded deviations in the direction orthogonal to this segment, and hence by Theorem A acts parabolically.…”

Section: Introductionmentioning

confidence: 98%

Parabolic isometries of the fine curve graph of the torus

Guihéneuf,

Militon

2024

Proceedings of London Math Soc

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Section: Introductionmentioning

confidence: 98%

Parabolic isometries of the fine curve graph of the torus

Guihéneuf,

Militon

2024

Proceedings of London Math Soc

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Non-existence of sublinear diffusion for a class of torus homeomorphisms

Salomão¹,

Tal²

2021

Ergod. Th. Dynam. Sys.

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Periodic point free homeomorphisms and irrational rotation factors

Kocsard¹

2020

Ergod. Th. Dynam. Sys.

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We provide a complete characterization of periodic point free homeomorphisms of the $2$ -torus admitting irrational circle rotations as topological factors. Given a homeomorphism of the $2$ -torus without periodic points and exhibiting uniformly bounded rotational deviations with respect to a rational direction, we show that annularity and the geometry of its non-wandering set are the only possible obstructions for the existence of an irrational circle rotation as topological factor. Through a very precise study of the dynamics of the induced $\rho $ -centralized skew-product, we extend and generalize considerably previous results of Jäger.

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Deviations in the Franks–Misiurewicz conjecture

Abstract: We show that if there exists a counter example for the rational case of the Franks-Misiurewicz conjecture, then it must exhibit unbounded deviations in the complementary direction of its rotation set.

Cited by 3 publications

References 17 publications

Parabolic isometries of the fine curve graph of the torus

Parabolic isometries of the fine curve graph of the torus

Non-existence of sublinear diffusion for a class of torus homeomorphisms

Periodic point free homeomorphisms and irrational rotation factors

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