Breaking of ergodicity in expanding systems of globally coupled piecewise affine circle maps

DOI10.1007/s10955-013-0903-9zbMath1371.37079OpenAlexW2056799801MaRDI QIDQ2016562

Bastien Fernandez

Publication date: 20 June 2014

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10955-013-0903-9

zbMATH Keywords

absolutely continuous invariant measurecoupled map latticebreaking of ergodicitypiecewise expanding dynamical system

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Dynamical systems involving maps of the circle (37E10) Phase transitions (general) in equilibrium statistical mechanics (82B26) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45)

Related Items (11)

Synchronization versus stability of the invariant distribution for a class of globally coupled maps ⋮ Mean-field coupling of identical expanding circle maps ⋮ Map lattices coupled by collisions: hitting time statistics and collisions per lattice unit ⋮ Symmetry breaking in a globally coupled map of four sites ⋮ Linear response for a family of self-consistent transfer operators ⋮ Conditioning problems for invariant sets of expanding piecewise affine mappings: application to loss of ergodicity in globally coupled maps ⋮ Self-consistent transfer operators: invariant measures, convergence to equilibrium, linear response and control of the statistical properties ⋮ Mean-field coupled systems and self-consistent transfer operators: a review ⋮ Globally coupled Anosov diffeomorphisms: statistical properties ⋮ Computer-assisted proof of loss of ergodicity by symmetry breaking in expanding coupled maps ⋮ Heterogeneously coupled maps: hub dynamics and emergence across connectivity layers

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