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Patterson–Sullivan theory for groups with a strongly contracting element

Part of: Dynamical systems with hyperbolic behavior Special aspects of infinite or finite groups Ergodic theory

Published online by Cambridge University Press:  05 March 2024

RÉMI COULON Open the ORCID record for RÉMI COULON [Opens in a new window]
RÉMI COULON*
Affiliation:
Université de Bourgogne, CNRS, IMB - UMR 5584, F-21000 Dijon, France
*
e-mail: remi.coulon@cnrs.fr
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Abstract

Using Patterson–Sullivan measures, we investigate growth problems for groups acting on a metric space with a strongly contracting element.

Keywords

Patterson–Sullivan measurescritical exponentgrowth ratecontracting elementamenability

MSC classification

Primary: 20F65: Geometric group theory 37D40: Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
Secondary: 57S30: Discontinuous groups of transformations 37A35: Entropy and other invariants, isomorphism, classification 37A15: General groups of measure-preserving transformations

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 44 , Issue 11 , November 2024 , pp. 3216 - 3271
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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