메뉴 건너뛰기




Volumn 60, Issue 5, 1999, Pages 6176-6179

Unstable periodic orbits and the natural measure of nonhyperbolic chaotic saddles

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE;

EID: 0001512843     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.60.6176     Document Type: Article
Times cited : (29)

References (41)
  • 3
    • 85036188544 scopus 로고    scopus 로고
    • T. Tél, in Directions in Chaos, edited by Bai-lin Hao (World Scientific, Singapore, 1990), Vol. 3;
    • T. Tél, in Directions in Chaos, edited by Bai-lin Hao (World Scientific, Singapore, 1990), Vol. 3
  • 4
    • 0004210476 scopus 로고    scopus 로고
    • Bai-lin Hao, World Scientific, Singapore
    • in STATPHYS 19, edited by Bai-lin Hao (World Scientific, Singapore, 1996).
    • (1996) STATPHYS 19
  • 6
    • 85036409711 scopus 로고    scopus 로고
    • Chaos 3 (1993), focus issue on chaotic scattering
    • Chaos 3 (1993), focus issue on chaotic scattering.
  • 16
    • 85036211786 scopus 로고    scopus 로고
    • At present, it is not clear how our work can be extended to higher dimensions due to the difficulties in the systematic computation of unstable periodic orbits
    • At present, it is not clear how our work can be extended to higher dimensions due to the difficulties in the systematic computation of unstable periodic orbits.
  • 17
    • 85036291219 scopus 로고    scopus 로고
    • The dynamics is hyperbolic on a chaotic set if at each point of the trajectory the phase space can be split into expanding and contracting subspaces and the angle between them is bounded away from zero. Furthermore, the expanding subspace evolves into expansion along the trajectory and the same is true for the contracting subspace. Otherwise the set is nonhyperbolic
    • The dynamics is hyperbolic on a chaotic set if at each point of the trajectory the phase space can be split into expanding and contracting subspaces and the angle between them is bounded away from zero. Furthermore, the expanding subspace evolves into expansion along the trajectory and the same is true for the contracting subspace. Otherwise the set is nonhyperbolic.
  • 18
    • 0020814903 scopus 로고
    • Chaotic saddles in Hamiltonian systems, on the other hand, are generally nonhyperbolic due to the presence of hierarchies of Kol’mogorov-Arnol’d-Moser (KAM) tori. Due to the stickiness effect of KAM tori, the decay of the number of chaotic trajectories in a phase-space region containing both the chaotic saddle and some KAM tori is algebraic in time [C. F. F. Karney, Physica D 8, 360 (1983)
    • (1983) Physica D , vol.8 , pp. 360
    • Karney, C.F.F.1
  • 29
    • 85036407278 scopus 로고    scopus 로고
    • dissipative systems, the sole source of nonhyperbolicity is the tangencies between the stable and the unstable manifolds. A trajectory on a nonhyperbolic chaotic saddle typically spends most of the time in regions where the dynamics is hyperbolic 13141516171820. Thus, we expect the decay of transient chaotic trajectories to be exponential [Eq. (1)] and the natural measure decays exponentially with the period as well [Eq. (6)]
    • In dissipative systems, the sole source of nonhyperbolicity is the tangencies between the stable and the unstable manifolds. A trajectory on a nonhyperbolic chaotic saddle typically spends most of the time in regions where the dynamics is hyperbolic 13141516171820. Thus, we expect the decay of transient chaotic trajectories to be exponential [Eq. (1)] and the natural measure decays exponentially with the period as well [Eq. (6)].
  • 32
    • 45149143640 scopus 로고
    • It is believed that the PIM-triple algorithm typically generates the natural measure of the chaotic saddle [H. E. Nusse and J. A. Yorke, Physica D 36, 137 (1989)
    • (1989) Physica D , vol.36 , pp. 137
    • Nusse, H.E.1    Yorke, J.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.