The differential of self-consistent transfer operators and the local convergence to equilibrium of mean field strongly coupled dynamical systems

2024/07/12 by Roberto Castorrini, Stefano Galatolo, Castorrini, Roberto +3 · 1 citation
Computer Science · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Advanced Thermodynamics and Statistical Mechanics #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Theoretical and Computational Physics

paper · doi:10.48550/arxiv.2407.09314

openalex publication_date 2024/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the differential of a self-consistent transfer operator at a fixed point of the operator itself and show that its spectral properties can be used to establish a kind of local exponential convergence to equilibrium: probability measures near the fixed point converge exponentially fast to the fixed point by the iteration of the transfer operator. This holds also in the strong coupling case. We also show that for mean field coupled systems satisfying uniformly a Lasota-Yorke inequality the differential does also. We present examples of application of the general results to self-consistent transfer operators based on deterministic expanding maps considered with different couplings, outside the weak coupling regime.

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• Selfconsistent Transfer Operators for Heterogeneous Coupled Maps

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