Unstable periodic orbits and the natural measure of nonhyperbolic chaotic saddles

Mukeshwar Dhamala, Ying-Cheng Lai

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

Chaotic saddles are nonattracting dynamical invariant sets that physically lead to transient chaos. We examine the characterization of the natural measure by unstable periodic orbits for nonhyperbolic chaotic saddles in dissipative dynamical systems. In particular, we compare the natural measure obtained from a long trajectory on the chaotic saddle to that evaluated from unstable periodic orbits embedded in it. Our systematic computations indicate that the periodic-orbit theory of the natural measure, previously shown to be valid only for hyperbolic chaotic sets, is applicable to nonhyperbolic chaotic saddles as well.

Original languageEnglish (US)
Pages (from-to)6176-6179
Number of pages4
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume60
Issue number5 B
StatePublished - Nov 1999
Externally publishedYes

Fingerprint

saddles
Saddle
Periodic Orbits
Unstable
orbits
Dissipative Dynamical System
dynamical systems
chaos
Invariant Set
trajectories
Chaos
Valid
Trajectory

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

@article{a21a42176493401f9f1d3535261a8890,
title = "Unstable periodic orbits and the natural measure of nonhyperbolic chaotic saddles",
abstract = "Chaotic saddles are nonattracting dynamical invariant sets that physically lead to transient chaos. We examine the characterization of the natural measure by unstable periodic orbits for nonhyperbolic chaotic saddles in dissipative dynamical systems. In particular, we compare the natural measure obtained from a long trajectory on the chaotic saddle to that evaluated from unstable periodic orbits embedded in it. Our systematic computations indicate that the periodic-orbit theory of the natural measure, previously shown to be valid only for hyperbolic chaotic sets, is applicable to nonhyperbolic chaotic saddles as well.",
author = "Mukeshwar Dhamala and Ying-Cheng Lai",
year = "1999",
month = "11",
language = "English (US)",
volume = "60",
pages = "6176--6179",
journal = "Physical Review E - Statistical, Nonlinear, and Soft Matter Physics",
issn = "1539-3755",
publisher = "American Physical Society",
number = "5 B",

}

TY - JOUR

T1 - Unstable periodic orbits and the natural measure of nonhyperbolic chaotic saddles

AU - Dhamala, Mukeshwar

AU - Lai, Ying-Cheng

PY - 1999/11

Y1 - 1999/11

N2 - Chaotic saddles are nonattracting dynamical invariant sets that physically lead to transient chaos. We examine the characterization of the natural measure by unstable periodic orbits for nonhyperbolic chaotic saddles in dissipative dynamical systems. In particular, we compare the natural measure obtained from a long trajectory on the chaotic saddle to that evaluated from unstable periodic orbits embedded in it. Our systematic computations indicate that the periodic-orbit theory of the natural measure, previously shown to be valid only for hyperbolic chaotic sets, is applicable to nonhyperbolic chaotic saddles as well.

AB - Chaotic saddles are nonattracting dynamical invariant sets that physically lead to transient chaos. We examine the characterization of the natural measure by unstable periodic orbits for nonhyperbolic chaotic saddles in dissipative dynamical systems. In particular, we compare the natural measure obtained from a long trajectory on the chaotic saddle to that evaluated from unstable periodic orbits embedded in it. Our systematic computations indicate that the periodic-orbit theory of the natural measure, previously shown to be valid only for hyperbolic chaotic sets, is applicable to nonhyperbolic chaotic saddles as well.

UR - http://www.scopus.com/inward/record.url?scp=0001512843&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001512843&partnerID=8YFLogxK

M3 - Article

VL - 60

SP - 6176

EP - 6179

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 5 B

ER -