Conditioning problems for invariant sets of expanding piecewise affine mappings: application to loss of ergodicity in globally coupled maps

DOI10.1088/1361-6544/ac640fzbMath1502.37004arXiv2008.04566OpenAlexW3048377049MaRDI QIDQ5089472

Bastien Fernandez, Fanni M. Sélley

Publication date: 19 July 2022

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.04566

zbMATH Keywords

dynamical systemsproofsloss of ergodicity

Mathematics Subject Classification ID

(n)-dimensional polytopes (52B11) Three-dimensional polytopes (52B10) Dynamical aspects of measure-preserving transformations (37A05) Ergodicity, mixing, rates of mixing (37A25) Polyhedra and polytopes; regular figures, division of spaces (51M20) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20)

Related Items (1)

Mean-field coupled systems and self-consistent transfer operators: a review

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Mean-field coupling of identical expanding circle maps
• Uniqueness of the SRB measure for piecewise expanding weakly coupled map lattices in any dimension
• Symmetry-increasing bifurcation of chaotic attractors
• A 'minimal', non-uniquely ergodic interval exchange transformation
• Non-ergodic interval exchange transformations
• Sinai-Bowen-Ruelle measures for certain Hénon maps
• Intrinsic ergodicity of affine maps in \([0,1^ d\)]
• Dynamics of piecewise isometries
• The synchronization of chaotic systems
• Symmetry breaking in a globally coupled map of four sites
• Breaking of ergodicity in expanding systems of globally coupled piecewise affine circle maps
• Computer-assisted proof of loss of ergodicity by symmetry breaking in expanding coupled maps
• Dynamics of coupled map lattices and of related spatially extended systems. Lectures delivered at the school-forum CML 2004, Paris, France, June 21 -- July 2, 2004.
• Piecewise isometries have zero topological entropy
• Transfer operators for coupled map lattices
• Phase transitions in a piecewise expanding coupled map lattice with linear nearest neighbour coupling
• Coupled map networks
• Convex Polytopes
• Coupled map lattices with phase transition
• Topological properties of linearly coupled expanding map lattices
• Spacetime chaos in coupled map lattices
• Interval exchange transformations
• Absolutely continuous invariant measures for expanding piecewise linear maps

This page was built for publication: Conditioning problems for invariant sets of expanding piecewise affine mappings: application to loss of ergodicity in globally coupled maps