August 20, 2025Proceedings of the American Mathematical Society0 citations

Quasi-isometric center action in dimension 3

MEMarcielis Espitia SMSantiago Martinchich RPRafaël Potrie

Key Points

The research establishes that diffeomorphisms are connected to skew-products or discretized Anosov flows.
Key findings indicate that diffeomorphisms act quasi-isometrically on a center foliation in three dimensions.
The study focuses on partially hyperbolic diffeomorphisms, analyzing their behavior through finite lift and iterate.
Understanding the nature of these diffeomorphisms may provide deeper insights into the dynamics of three-dimensional systems.

Abstract

We study transitive partially hyperbolic diffeomorphisms in dimension 3 preserving a center foliation on which they act quasi-isometrically. We show that the diffeomorphism is up to finite lift and iterate, either a skew-product or a discretized Anosov flow.

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Cite This Study

Espitia et al. (Wed,) studied this question.

synapsesocial.com/papers/68af4cd8ad7bf08b1ead63ce https://doi.org/https://doi.org/10.1090/proc/17319

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