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Linear response due to singularities

journal contribution
posted on 2024-05-14, 13:52 authored by Wael BahsounWael Bahsoun, Stefano Galatolo
It is well known that a family of tent-like maps with bounded derivatives has no linear response for typical deterministic perturbations changing the value of the turning point. In this note we prove the following result: if we consider a tent-like family with a cusp at the turning point, we recover the linear response. More precisely, let Tε be a family of such cusp maps generated by changing the value of the turning point of T0 by a deterministic perturbation and let hε be the corresponding invariant density. We prove that ε 7→ hε is differentiable in L1 and provide a formula for its derivative.

Funding

Transfer operators and emergent dynamics in hyperbolic systems

Engineering and Physical Sciences Research Council

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History

School

  • Science

Department

  • Mathematical Sciences

Published in

Nonlinearity

Publisher

IOP Publishing

Version

  • AM (Accepted Manuscript)

Publisher statement

This is the Accepted Manuscript version of an article accepted for publication in Nonlinearity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at [insert DOI].

Acceptance date

2024-05-09

ISSN

0951-7715

eISSN

1361-6544

Language

  • en

Depositor

Prof Wael Bahsoun. Deposit date: 9 May 2024

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