Linear Response for Intermittent Circle Maps

TL;DR

This paper demonstrates linear response and statistical stability for intermittent circle maps by applying the Cone technique to analyze the weak differentiability of the SRB measure.

Contribution

It introduces a novel application of the Cone technique to establish linear response and stability in intermittent circle maps.

Findings

Weak differentiability of SRB measure established

Linear response demonstrated for intermittent maps

Statistical stability of solenoid maps with intermittency shown

Abstract

Using the Cone technique of Baladi and Todd, we show some form of weak differentiability of the SRB measure for the intermittent circle maps, demonstrating linear response in the process. Subsequently, as an application, we lift the regularity from the base dynamics of the solenoid map with intermittency, showing that this family is statistically stable.