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Mean field coupled dynamical systems: Bifurcations and phase transitions

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posted on 2025-02-04, 13:43 authored by Wael BahsounWael Bahsoun, Carlangelo Liverani

We develop a bifurcation theory for infinite dimensional systems satisfying abstract hypotheses that are tailored for applications to mean field coupled chaotic maps. Our abstract theory can be applied to many cases, from globally coupled expanding maps to globally coupled Axiom A diffeomorphisms. To illustrate the range of applicability, we analyze an explicit example consisting of globally coupled Anosov diffeomorphisms. For such an example, we classify all the invariant measures as the coupling strength varies; we show which invariant measures are physical, and we prove that the existence of multiple invariant physical measures is a purely infinite dimensional phenomenon, i.e., the model exhibits phase transitions in the sense of statistical mechanics.

Funding

OTH Transfer operators and emergent dynamics in hyperbolic systems

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Advances in Mathematics

Volume

463

Issue

2025

Publisher

Elsevier

Version

  • VoR (Version of Record)

Rights holder

© The Author(s)

Publisher statement

This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)

Acceptance date

2025-01-11

Publication date

2025-01-21

Copyright date

2025

ISSN

0001-8708

Language

  • en

Depositor

Prof Wael Bahsoun. Deposit date: 12 January 2025

Article number

110115

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