Classification of partially hyperbolic surface endomorphisms

Layne Hall; Andy Hammerlindl

doi:10.1007/s10711-022-00684-9

Classification of partially hyperbolic surface endomorphisms

Layne Hall, Andy Hammerlindl

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

Abstract

We show that in the absence of periodic centre annuli, a partially hyperbolic surface endomorphism is dynamically coherent and leaf conjugate to its linearisation. We proceed to characterise the dynamics in the presence of periodic centre annuli. This completes a classification of partially hyperbolic surface endomorphisms.

Original language	English
Article number	29
Number of pages	19
Journal	Geometriae Dedicata
Volume	216
Issue number	3
DOIs	https://doi.org/10.1007/s10711-022-00684-9
Publication status	Published - Jun 2022

Keywords

Dynamical coherence
Non-invertible dynamics
Partial hyperbolicity

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title = "Classification of partially hyperbolic surface endomorphisms",

abstract = "We show that in the absence of periodic centre annuli, a partially hyperbolic surface endomorphism is dynamically coherent and leaf conjugate to its linearisation. We proceed to characterise the dynamics in the presence of periodic centre annuli. This completes a classification of partially hyperbolic surface endomorphisms.",

keywords = "Dynamical coherence, Non-invertible dynamics, Partial hyperbolicity",

author = "Layne Hall and Andy Hammerlindl",

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Classification of partially hyperbolic surface endomorphisms

Abstract

Keywords

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