A3 Book section, Chapters in research books
Rate of Mixing for Equilibrium States in Negative Curvature and Trees (2021)
Broise-Alamichel, A., Parkkonen, J., & Paulin, F. (2021). Rate of Mixing for Equilibrium States in Negative Curvature and Trees. In M. Pollicott, & S. Vaienti (Eds.), Thermodynamic Formalism : CIRM Jean-Morlet Chair, Fall 2019 (pp. 291-315). Springer. Lecture Notes in Mathematics, 2290. https://doi.org/10.1007/978-3-030-74863-0_9
JYU authors or editors
Publication details
All authors or editors: Broise-Alamichel, Anne; Parkkonen, Jouni; Paulin, Frédéric
Parent publication: Thermodynamic Formalism : CIRM Jean-Morlet Chair, Fall 2019
Parent publication editors: Pollicott, Mark; Vaienti, Sandro
ISBN: 978-3-030-74862-3
eISBN: 978-3-030-74863-0
Journal or series: Lecture Notes in Mathematics
ISSN: 0075-8434
eISSN: 1617-9692
Publication year: 2021
Number in series: 2290
Pages range: 291-315
Number of pages in the book: 536
Publisher: Springer
Place of Publication: Cham
Publication country: Switzerland
Publication language: English
DOI: https://doi.org/10.1007/978-3-030-74863-0_9
Publication open access: Not open
Publication channel open access:
Web address of parallel published publication (pre-print): https://arxiv.org/abs/2010.08212
Abstract
In this survey based on the recent book by the three authors, we recall the Patterson-Sullivan construction of equilibrium states for the geodesic flow on negatively curved orbifolds or tree quotients, and discuss their mixing properties, emphasizing the rate of mixing for (not necessarily compact) tree quotients via coding by countable (not necessarily finite) topological shifts. We give a new construction of numerous nonuniform tree lattices such that the (discrete time) geodesic flow on the tree quotient is exponentially mixing with respect to the maximal entropy measure: we construct examples whose tree quotients have an arbitrary space of ends or an arbitrary (at most exponential) growth type.
Keywords: dynamical systems
Free keywords: equilibrium state; Gibbs measure; negative curvature; geodesic flow; mixing; trees; coding; rate of mixing; tree lattices
Contributing organizations
Ministry reporting: Yes
Reporting Year: 2021
JUFO rating: 1
