Classification of partially hyperbolic surface endomorphisms
Layne Hall, Andy Hammerlindl
TL;DR
This paper classifies partially hyperbolic surface endomorphisms, demonstrating their coherence and conjugacy to linear models when no periodic centre annuli are present, and analyzing dynamics when such annuli exist.
Contribution
It provides a complete classification of these endomorphisms, including cases with and without periodic centre annuli, extending previous partial results.
Findings
Dynamically coherent and leaf conjugate to linearisation without periodic centre annuli
Characterization of dynamics with periodic centre annuli
Complete 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.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Quantum chaos and dynamical systems · Geometric and Algebraic Topology