Devil-staircase behavior of dynamical invariants in chaotic scattering

Karol Zyczkowski; Ying-Cheng Lai

doi:10.1016/S0167-2789(00)00059-2

Devil-staircase behavior of dynamical invariants in chaotic scattering

Research output: Contribution to journal › Article › peer-review

Abstract

A crisis in chaotic scattering is characterized by the merging of two or more nonattracting chaotic saddles. The fractal dimension of the resulting chaotic saddle increases through the crisis. We present a rigorous analysis for the behavior of dynamical invariants associated with chaotic scattering by utilizing a representative model system that captures the essential dynamical features of crisis. Our analysis indicates that the fractal dimension and other dynamical invariants are a devil-staircase type of function of the system parameter. Our results can also provide insight for similar devil-staircase behaviors observed in the parametric evolution of chaotic saddles of general dissipative dynamical systems and in communicating with chaos.

Original language	English (US)
Pages (from-to)	197-216
Number of pages	20
Journal	Physica D: Nonlinear Phenomena
Volume	142
Issue number	3-4
DOIs	https://doi.org/10.1016/S0167-2789(00)00059-2
State	Published - Aug 15 2000

Keywords

Chaotic scattering
Devil staircase
Dynamical invariants

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/S0167-2789(00)00059-2

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title = "Devil-staircase behavior of dynamical invariants in chaotic scattering",

abstract = "A crisis in chaotic scattering is characterized by the merging of two or more nonattracting chaotic saddles. The fractal dimension of the resulting chaotic saddle increases through the crisis. We present a rigorous analysis for the behavior of dynamical invariants associated with chaotic scattering by utilizing a representative model system that captures the essential dynamical features of crisis. Our analysis indicates that the fractal dimension and other dynamical invariants are a devil-staircase type of function of the system parameter. Our results can also provide insight for similar devil-staircase behaviors observed in the parametric evolution of chaotic saddles of general dissipative dynamical systems and in communicating with chaos.",

keywords = "Chaotic scattering, Devil staircase, Dynamical invariants",

author = "Karol Zyczkowski and Ying-Cheng Lai",

note = "Funding Information: We thank Prof. E. Bollt, Prof. C. Grebogi, and Dr. W. S{\l}omczy{\'n}ski for helpful discussions. K{\.Z} acknowledges the Fulbright Fellowship, a support by Polski Komitet Bada{\'n} Naukowych and is grateful to Prof. E. Ott for hospitality at the Institute for Plasma Physics, University of Maryland, where this work has been initiated. YCL was supported by NSF under Grant No. PHY-9722156 and by AFOSR under Grant No. F49620-98-1-0400.",

year = "2000",

month = aug,

day = "15",

doi = "10.1016/S0167-2789(00)00059-2",

language = "English (US)",

volume = "142",

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TY - JOUR

T1 - Devil-staircase behavior of dynamical invariants in chaotic scattering

AU - Zyczkowski, Karol

AU - Lai, Ying-Cheng

N1 - Funding Information: We thank Prof. E. Bollt, Prof. C. Grebogi, and Dr. W. Słomczyński for helpful discussions. KŻ acknowledges the Fulbright Fellowship, a support by Polski Komitet Badań Naukowych and is grateful to Prof. E. Ott for hospitality at the Institute for Plasma Physics, University of Maryland, where this work has been initiated. YCL was supported by NSF under Grant No. PHY-9722156 and by AFOSR under Grant No. F49620-98-1-0400.

PY - 2000/8/15

Y1 - 2000/8/15

N2 - A crisis in chaotic scattering is characterized by the merging of two or more nonattracting chaotic saddles. The fractal dimension of the resulting chaotic saddle increases through the crisis. We present a rigorous analysis for the behavior of dynamical invariants associated with chaotic scattering by utilizing a representative model system that captures the essential dynamical features of crisis. Our analysis indicates that the fractal dimension and other dynamical invariants are a devil-staircase type of function of the system parameter. Our results can also provide insight for similar devil-staircase behaviors observed in the parametric evolution of chaotic saddles of general dissipative dynamical systems and in communicating with chaos.

AB - A crisis in chaotic scattering is characterized by the merging of two or more nonattracting chaotic saddles. The fractal dimension of the resulting chaotic saddle increases through the crisis. We present a rigorous analysis for the behavior of dynamical invariants associated with chaotic scattering by utilizing a representative model system that captures the essential dynamical features of crisis. Our analysis indicates that the fractal dimension and other dynamical invariants are a devil-staircase type of function of the system parameter. Our results can also provide insight for similar devil-staircase behaviors observed in the parametric evolution of chaotic saddles of general dissipative dynamical systems and in communicating with chaos.

KW - Chaotic scattering

KW - Devil staircase

KW - Dynamical invariants

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U2 - 10.1016/S0167-2789(00)00059-2

DO - 10.1016/S0167-2789(00)00059-2

M3 - Article

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SN - 0167-2789

VL - 142

SP - 197

EP - 216

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 3-4

ER -

Devil-staircase behavior of dynamical invariants in chaotic scattering

Abstract

Keywords

ASJC Scopus subject areas

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