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arXiv · 2001.01317

Linear Response for a Family of Self-Consistent Transfer Operators

Fanni M. Sélley·Matteo Tanzi
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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.

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Fanni M. Sélley, Matteo Tanzi. 2020-01-05. Linear Response for a Family of Self-Consistent Transfer Operators. https://doi.org/10.1007/s00220-021-03983-6

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