Mean field coupled dynamical systems: Bifurcations and phase transitions
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 MathematicsVolume
463Issue
2025Publisher
ElsevierVersion
- 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
2025-01-11Publication date
2025-01-21Copyright date
2025ISSN
0001-8708Publisher version
Language
- en