Linear Response for a Family of Self-Consistent Transfer Operators

Abstract

We study a system of all-to-all weakly coupled uniformly expanding circle maps in the thermodynamic limit. The state of the system is described by a probability measure and its evolution is given by the action of a nonlinear operator, also called a self-consistent transfer operator. We prove that when the coupling is sufficiently small, the system has a unique stable state that satisfies a linear response formula when varying the coupling strength.

Electronic copy of final peer-reviewed manuscript accepted for publication

References in corpus (4)

• A review of linear response theory for general differentiable dynamical systems
• On the susceptibility function of piecewise expanding interval maps
• Linear response for macroscopic observables in high-dimensional systems
• Quadratic response of random and deterministic dynamical systems

Cited by in corpus (5)

• Self consistent transfer operators. Invariant measures, convergence to equilibrium, linear response and control of the statistical properties
• Globally coupled Anosov diffeomorphisms: Statistical properties
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• Mean-field and fluctuations for hub dynamics in heterogeneous random networks