Linear Response for a Family of Self-Consistent Transfer Operators

Linear Response for a Family of Self-Consistent Transfer Operators

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 wh...

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Veröffentlicht in:arXiv.org 2021-01
Hauptverfasser: Sélley, Fanni M, Tanzi, Matteo
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Coupling
Mathematics - Dynamical Systems
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description 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.
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title Linear Response for a Family of Self-Consistent Transfer Operators
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