Galatolo, Stefano and Pollicott, Mark (2017) Controlling the statistical properties of expanding maps. Nonlinearity, 30 . 2737. ISSN 0951-7715.

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Abstract

How can one change a system, in order to change its statistical properties in a prescribed way? In this note we consider a control problem related to the theory of linear response. Given an expanding map of the unit circle with an associated invariant density we can consider the inverse problem of finding which first order changes in the transformation can achieve a given first order perturbation in the density. We show the general mathematical structure of the problem, the existence of many solutions in the case of expanding maps of the circle and the existence of optimal ones. We investigate in depth the example of the doubling map, where we give a complete solution of the problem.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Mappings (Mathematics), Mathematical statistics
Journal or Publication Title:	Nonlinearity
Publisher:	Institute of Physics Publishing Ltd.
ISSN:	0951-7715
Official Date:	26 May 2017
Dates:	Date Event 26 May 2017 Published 2 May 2017 Accepted
Volume:	30
Article Number:	2737
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	4 May 2017
Date of first compliant Open Access:	26 May 2018
RIOXX Funder/Project Grant:	Project/Grant ID RIOXX Funder Name Funder ID Network Grant IN-2014-021 Leverhulme Trust http://dx.doi.org/10.13039/501100000275

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