A new approach to the treatment of separatrix chaos and its applications.

Physics

Associated organisational unit

Nonlinear and Biomedical Physics

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter

Published

Standard

A new approach to the treatment of separatrix chaos and its applications. / Soskin, Stanislav M.; Mannella, R.; Yevtushenko, O. M. et al.
Hamiltonian Chaos Beyond the KAM Theory. ed. / A. C. J. Luo; V. Afraimovich. Beijng and Heidelberg: Higher Education Press and Springer, 2010. p. 51-141 (Nonlinear Physical Science).

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter

Harvard

Soskin, SM, Mannella, R, Yevtushenko, OM, Khovanov, IA & McClintock, PVE 2010, A new approach to the treatment of separatrix chaos and its applications. in ACJ Luo & V Afraimovich (eds), Hamiltonian Chaos Beyond the KAM Theory. Nonlinear Physical Science, Higher Education Press and Springer, Beijng and Heidelberg, pp. 51-141.

APA

Soskin, S. M., Mannella, R., Yevtushenko, O. M., Khovanov, I. A., & McClintock, P. V. E. (2010). A new approach to the treatment of separatrix chaos and its applications. In A. C. J. Luo, & V. Afraimovich (Eds.), Hamiltonian Chaos Beyond the KAM Theory (pp. 51-141). (Nonlinear Physical Science). Higher Education Press and Springer.

Vancouver

Soskin SM, Mannella R, Yevtushenko OM, Khovanov IA , McClintock PVE. A new approach to the treatment of separatrix chaos and its applications. In Luo ACJ, Afraimovich V, editors, Hamiltonian Chaos Beyond the KAM Theory. Beijng and Heidelberg: Higher Education Press and Springer. 2010. p. 51-141. (Nonlinear Physical Science).

Author

Soskin, Stanislav M. ; Mannella, R. ; Yevtushenko, O. M. et al. / A new approach to the treatment of separatrix chaos and its applications. Hamiltonian Chaos Beyond the KAM Theory. editor / A. C. J. Luo ; V. Afraimovich. Beijng and Heidelberg : Higher Education Press and Springer, 2010. pp. 51-141 (Nonlinear Physical Science).

Bibtex

@inbook{ad1ab02524214382bd5261e50f116ba1,

title = "A new approach to the treatment of separatrix chaos and its applications.",

abstract = "We consider time-periodically perturbed ID Hamiltonian systems possessing one or more separatrices. If the perturbation is weak, then the separatrix chaos is most developed when the perturbation frequency lies in the logarithmically small or moderate ranges: this corresponds to the involvement of resonance dynamics into the separatrix chaos. We develop a method matching the discrete chaotic dynamics of the separatrix map and the continuous regular dynamics of the resonance Hamiltonian. The method has allowed us to solve the long-standing problem of an accurate description of the maximum of the separatrix chaotic layer width as a function of the perturbation frequency. It has also allowed us to predict and describe new phenomena including, in particular: (i) a drastic facilitation of the onset of global chaos between neighbouring separatrices, and (ii) a huge increase in the size of the low-dimensional stochastic web.",

author = "Soskin, {Stanislav M.} and R. Mannella and Yevtushenko, {O. M.} and Khovanov, {I. A.} and McClintock, {P. V. E.}",

year = "2010",

language = "English",

isbn = "978-3-642-12717-5",

series = "Nonlinear Physical Science",

publisher = "Higher Education Press and Springer",

pages = "51--141",

editor = "Luo, {A. C. J.} and V. Afraimovich",

booktitle = "Hamiltonian Chaos Beyond the KAM Theory",

}

RIS

TY - CHAP

T1 - A new approach to the treatment of separatrix chaos and its applications.

AU - Soskin, Stanislav M.

AU - Mannella, R.

AU - Yevtushenko, O. M.

AU - Khovanov, I. A.

AU - McClintock, P. V. E.

PY - 2010

Y1 - 2010

N2 - We consider time-periodically perturbed ID Hamiltonian systems possessing one or more separatrices. If the perturbation is weak, then the separatrix chaos is most developed when the perturbation frequency lies in the logarithmically small or moderate ranges: this corresponds to the involvement of resonance dynamics into the separatrix chaos. We develop a method matching the discrete chaotic dynamics of the separatrix map and the continuous regular dynamics of the resonance Hamiltonian. The method has allowed us to solve the long-standing problem of an accurate description of the maximum of the separatrix chaotic layer width as a function of the perturbation frequency. It has also allowed us to predict and describe new phenomena including, in particular: (i) a drastic facilitation of the onset of global chaos between neighbouring separatrices, and (ii) a huge increase in the size of the low-dimensional stochastic web.

AB - We consider time-periodically perturbed ID Hamiltonian systems possessing one or more separatrices. If the perturbation is weak, then the separatrix chaos is most developed when the perturbation frequency lies in the logarithmically small or moderate ranges: this corresponds to the involvement of resonance dynamics into the separatrix chaos. We develop a method matching the discrete chaotic dynamics of the separatrix map and the continuous regular dynamics of the resonance Hamiltonian. The method has allowed us to solve the long-standing problem of an accurate description of the maximum of the separatrix chaotic layer width as a function of the perturbation frequency. It has also allowed us to predict and describe new phenomena including, in particular: (i) a drastic facilitation of the onset of global chaos between neighbouring separatrices, and (ii) a huge increase in the size of the low-dimensional stochastic web.

M3 - Chapter

SN - 978-3-642-12717-5

T3 - Nonlinear Physical Science

SP - 51

EP - 141

BT - Hamiltonian Chaos Beyond the KAM Theory

A2 - Luo, A. C. J.

A2 - Afraimovich, V.

PB - Higher Education Press and Springer

CY - Beijng and Heidelberg

ER -

Research

Associated organisational unit