LIMIT THEOREMS FOR COUPLED INTERVAL MAPS

DOI10.1142/S0219493707001913zbMath1114.37006arXivmath/0609639MaRDI QIDQ3439929

Gerhard Keller, Jean-Baptiste Bardet, Sébastien Gouëzel

Publication date: 21 May 2007

Published in: Stochastics and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0609639

zbMATH Keywords

spectral gapcoupled map latticelocal limit theorempiecewise expanding map

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Ergodic theorems, spectral theory, Markov operators (37A30) Lattice dynamics and infinite-dimensional dissipative dynamical systems (37L60) Dynamical systems involving maps of the interval (37E05)

Related Items (9)

Rare events, exponential hitting times and extremal indices via spectral perturbation† ⋮ Fluctuations of Observables in Dynamical Systems: From Limit Theorems to Concentration Inequalities ⋮ Small eigenvalues of the Laplacian for algebraic measures in moduli space, and mixing properties of the Teichmüller flow ⋮ Mean-field coupled systems and self-consistent transfer operators: a review ⋮ A local limit theorem for a transient chaotic walk in a frozen environment ⋮ Almost sure invariance principle for dynamical systems by spectral methods ⋮ Coupled iterated function systems that contract on average ⋮ Local limit theorem for nonuniformly partially hyperbolic skew-products and Farey sequences ⋮ Map lattices coupled by collisions

Cites Work

• Unnamed Item
• Uniqueness of the SRB measure for piecewise expanding weakly coupled map lattices in any dimension
• Equilibrium measures for coupled map lattices: Existence, uniqueness and finite-dimensional approximations
• Limit theorems for coupled analytic maps
• The rate of convergence in ergodic theorems
• Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness

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