Linear Response for a Family of Self-Consistent Transfer Operators
Dynamical Systems
2022-09-22 v3
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.
Cite
@article{arxiv.2001.01317,
title = {Linear Response for a Family of Self-Consistent Transfer Operators},
author = {Fanni M. Sélley and Matteo Tanzi},
journal= {arXiv preprint arXiv:2001.01317},
year = {2022}
}
Comments
Electronic copy of final peer-reviewed manuscript accepted for publication