St Andrews Research Repository

St Andrews University Home
View Item 
  •   St Andrews Research Repository
  • University of St Andrews Research
  • University of St Andrews Research
  • University of St Andrews Research
  • View Item
  •   St Andrews Research Repository
  • University of St Andrews Research
  • University of St Andrews Research
  • University of St Andrews Research
  • View Item
  •   St Andrews Research Repository
  • University of St Andrews Research
  • University of St Andrews Research
  • University of St Andrews Research
  • View Item
  • Register / Login
JavaScript is disabled for your browser. Some features of this site may not work without it.

Slow and fast escape for open intermittent maps

Thumbnail
View/Open
MPcim_submit2.pdf (644.9Kb)
Date
04/2017
Author
Demers, Mark F.
Todd, Mike
Keywords
QA Mathematics
QC Physics
T-NDAS
BDC
R2C
Metadata
Show full item record
Abstract
If a system mixes too slowly, putting a hole in it can completely destroy the richness of the dynamics. Here we study this instability for a class of intermittent maps with a family of slowly mixing measures. We show that there are three regimes: (1) standard hyperbolic-like behavior where the rate of mixing is faster than the rate of escape through the hole, there is a unique limiting absolutely continuous conditionally invariant measure (accim) and there is a complete thermodynamic description of the dynamics on the survivor set; (2) an intermediate regime, where the rate of mixing and escape through the hole coincide, limiting accims exist, but much of the thermodynamic picture breaks down; (3) a subexponentially mixing regime where the slow mixing means that mass simply accumulates on the parabolic fixed point. We give a complete picture of the transitions and stability properties (in the size of the hole and as we move through the family) in this class of open systems. In particular, we are able to recover a form of stability in the third regime above via the dynamics on the survivor set, even when no limiting accim exists.
Citation
Demers , M F & Todd , M 2017 , ' Slow and fast escape for open intermittent maps ' , Communications in Mathematical Physics , vol. 351 , no. 2 , pp. 775-835 . https://doi.org/10.1007/s00220-017-2829-6
Publication
Communications in Mathematical Physics
Status
Peer reviewed
DOI
https://doi.org/10.1007/s00220-017-2829-6
ISSN
0010-3616
Type
Journal article
Rights
© 2017, Springer-Verlag Berlin Heidelberg. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at link.springer.com / https://doi.org/10.1007/s00220-017-2829-6
Description
MD was partially supported by NSF grant DMS 1362420. This project was started as part of an RiGs grant through ICMS, Scotland.
Collections
  • University of St Andrews Research
URI
http://hdl.handle.net/10023/12658

Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.

Advanced Search

Browse

All of RepositoryCommunities & CollectionsBy Issue DateNamesTitlesSubjectsClassificationTypeFunderThis CollectionBy Issue DateNamesTitlesSubjectsClassificationTypeFunder

My Account

Login

Open Access

To find out how you can benefit from open access to research, see our library web pages and Open Access blog. For open access help contact: openaccess@st-andrews.ac.uk.

Accessibility

Read our Accessibility statement.

How to submit research papers

The full text of research papers can be submitted to the repository via Pure, the University's research information system. For help see our guide: How to deposit in Pure.

Electronic thesis deposit

Help with deposit.

Repository help

For repository help contact: Digital-Repository@st-andrews.ac.uk.

Give Feedback

Cookie policy

This site may use cookies. Please see Terms and Conditions.

Usage statistics

COUNTER-compliant statistics on downloads from the repository are available from the IRUS-UK Service. Contact us for information.

© University of St Andrews Library

University of St Andrews is a charity registered in Scotland, No SC013532.

  • Facebook
  • Twitter