On-off intermittency and chaotic walks

Ale Jan Homburg, Vahatra Rabodonandrianandraina

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

We consider a class of skew product maps of interval diffeomorphisms over the doubling map. The interval maps fix the end points of the interval. It is assumed that the system has zero fiber Lyapunov exponent at one endpoint and zero or positive fiber Lyapunov exponent at the other endpoint. We prove the appearance of on-off intermittency. This is done using the equivalent description of chaotic walks: random walks driven by the doubling map. The analysis further relies on approximating the chaotic walks by Markov random walks, that are constructed using Markov partitions for the doubling map.

Original languageEnglish
Pages (from-to)1-38
Number of pages38
JournalErgodic theory and dynamical systems
DOIs
Publication statusE-pub ahead of print - 30 Jan 2019

Fingerprint

Intermittency
Walk
Doubling
Lyapunov Exponent
Random walk
Fiber
Markov Partition
Interval Maps
Skew Product
Interval
Zero
End point
Diffeomorphisms
Fibers

Keywords

  • 2010 Mathematics Subject Classification
  • 37C40 (Primary)
  • 37D25
  • 37H20 (Secondary)

Cite this

Homburg, Ale Jan ; Rabodonandrianandraina, Vahatra. / On-off intermittency and chaotic walks. In: Ergodic theory and dynamical systems. 2019 ; pp. 1-38.
@article{905ca83093be4d56a0a375695e3d2d43,
title = "On-off intermittency and chaotic walks",
abstract = "We consider a class of skew product maps of interval diffeomorphisms over the doubling map. The interval maps fix the end points of the interval. It is assumed that the system has zero fiber Lyapunov exponent at one endpoint and zero or positive fiber Lyapunov exponent at the other endpoint. We prove the appearance of on-off intermittency. This is done using the equivalent description of chaotic walks: random walks driven by the doubling map. The analysis further relies on approximating the chaotic walks by Markov random walks, that are constructed using Markov partitions for the doubling map.",
keywords = "2010 Mathematics Subject Classification, 37C40 (Primary), 37D25, 37H20 (Secondary)",
author = "Homburg, {Ale Jan} and Vahatra Rabodonandrianandraina",
year = "2019",
month = "1",
day = "30",
doi = "10.1017/etds.2018.142",
language = "English",
pages = "1--38",
journal = "Ergodic theory and dynamical systems",
issn = "0143-3857",
publisher = "Cambridge University Press",

}

On-off intermittency and chaotic walks. / Homburg, Ale Jan; Rabodonandrianandraina, Vahatra.

In: Ergodic theory and dynamical systems, 30.01.2019, p. 1-38.

Research output: Contribution to JournalArticleAcademicpeer-review

TY - JOUR

T1 - On-off intermittency and chaotic walks

AU - Homburg, Ale Jan

AU - Rabodonandrianandraina, Vahatra

PY - 2019/1/30

Y1 - 2019/1/30

N2 - We consider a class of skew product maps of interval diffeomorphisms over the doubling map. The interval maps fix the end points of the interval. It is assumed that the system has zero fiber Lyapunov exponent at one endpoint and zero or positive fiber Lyapunov exponent at the other endpoint. We prove the appearance of on-off intermittency. This is done using the equivalent description of chaotic walks: random walks driven by the doubling map. The analysis further relies on approximating the chaotic walks by Markov random walks, that are constructed using Markov partitions for the doubling map.

AB - We consider a class of skew product maps of interval diffeomorphisms over the doubling map. The interval maps fix the end points of the interval. It is assumed that the system has zero fiber Lyapunov exponent at one endpoint and zero or positive fiber Lyapunov exponent at the other endpoint. We prove the appearance of on-off intermittency. This is done using the equivalent description of chaotic walks: random walks driven by the doubling map. The analysis further relies on approximating the chaotic walks by Markov random walks, that are constructed using Markov partitions for the doubling map.

KW - 2010 Mathematics Subject Classification

KW - 37C40 (Primary)

KW - 37D25

KW - 37H20 (Secondary)

UR - http://www.scopus.com/inward/record.url?scp=85060893108&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85060893108&partnerID=8YFLogxK

U2 - 10.1017/etds.2018.142

DO - 10.1017/etds.2018.142

M3 - Article

SP - 1

EP - 38

JO - Ergodic theory and dynamical systems

JF - Ergodic theory and dynamical systems

SN - 0143-3857

ER -