Work

Patterson-Sullivan theory for coarse cocycles

Year: 2024

Type: preprint

Abstract: In this paper we develop a theory of Patterson--Sullivan measures associated to coarse cocycles of convergence groups. This framework includes Patterson-Sullivan measures associated to the Busemann cocycle on the geodesic boundary of a Gromov hyperbolic metric spaces and Patterson-Sullivan measures on flag manifolds associated to Anosov (or more general transverse) subgroups of semisimple Lie groups, as well as more examples. Under some natural geometric assumptions on the coarse cocycle, we prove existence, uniqueness, and ergodicity results.

Source: HAL (Le Centre pour la Communication Scientifique Directe)

DOI: 10.48550/arxiv.2404.09713

Authors: Blayac, Pierre-Louis, Canary, Richard, Zhu, Feng, Zimmer, Andrew

Institutions: University of Wisconsin–Madison, University of Michigan, Institut de Recherche Mathématique Avancée

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: CAREER: Intrinsic and Extrinsic Conditions in Several Complex Variables, Deformation spaces of geometric structures

OpenAlex ID: W4394896845

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