Chaotic systems in complex phase space

Carl M. Bender; Joshua Feinberg; Daniel W. Hook; David J. Weir

doi:10.1007/s12043-009-0099-3

Chaotic systems in complex phase space

Carl M. Bender, Joshua Feinberg, Daniel W. Hook, David J. Weir

Department of Physics

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

Abstract

This paper examines numerically the complex classical trajectories of the kicked rotor and the double pendulum. Both of these systems exhibit a transition to chaos, and this feature is studied in complex phase space. Additionally, it is shown that the short-time and long-time behaviours of these two PT -symmetric dynamical models in complex phase space exhibit strong qualitative similarities.

Original language	English
Pages (from-to)	453-470
Number of pages	18
Journal	Pramana - Journal of Physics
Volume	73
Issue number	3
DOIs	https://doi.org/10.1007/s12043-009-0099-3
State	Published - Sep 2009

Bibliographical note

Funding Information:
We thank S Fishman and F Leyvraz for discussions and I Guarnery for bringing ref. [27] to our attention. CMB is supported by the U.S. Department of Energy. JF thanks the KITP at UC Santa Barbara for its hospitality while this paper was completed. His research at the KITP was supported in part by the National Science Foundation under Grant No. PHY05-51164. DWH is supported by Symplectic Ltd. DJW thanks the Imperial College High Performance Computing Service, URL: http: // www.imperial.ac.uk / ict/services / teachingandresearchservices/highperfor-mancecomputing.

Keywords

Approach to chaos
Double pendulum
Kicked rotor
PT symmetry
Standard map

ASJC Scopus subject areas

General Physics and Astronomy

Access to Document

10.1007/s12043-009-0099-3

Cite this

@article{eb39df179f204afdba30c6e452d69e74,

title = "Chaotic systems in complex phase space",

abstract = "This paper examines numerically the complex classical trajectories of the kicked rotor and the double pendulum. Both of these systems exhibit a transition to chaos, and this feature is studied in complex phase space. Additionally, it is shown that the short-time and long-time behaviours of these two PT -symmetric dynamical models in complex phase space exhibit strong qualitative similarities.",

keywords = "Approach to chaos, Double pendulum, Kicked rotor, PT symmetry, Standard map",

author = "Bender, {Carl M.} and Joshua Feinberg and Hook, {Daniel W.} and Weir, {David J.}",

note = "Funding Information: We thank S Fishman and F Leyvraz for discussions and I Guarnery for bringing ref. [27] to our attention. CMB is supported by the U.S. Department of Energy. JF thanks the KITP at UC Santa Barbara for its hospitality while this paper was completed. His research at the KITP was supported in part by the National Science Foundation under Grant No. PHY05-51164. DWH is supported by Symplectic Ltd. DJW thanks the Imperial College High Performance Computing Service, URL: http: // www.imperial.ac.uk / ict/services / teachingandresearchservices/highperfor-mancecomputing.",

year = "2009",

month = sep,

doi = "10.1007/s12043-009-0099-3",

language = "English",

volume = "73",

pages = "453--470",

journal = "Pramana - Journal of Physics",

issn = "0304-4289",

publisher = "Springer India",

number = "3",

}

TY - JOUR

T1 - Chaotic systems in complex phase space

AU - Bender, Carl M.

AU - Feinberg, Joshua

AU - Hook, Daniel W.

AU - Weir, David J.

N1 - Funding Information: We thank S Fishman and F Leyvraz for discussions and I Guarnery for bringing ref. [27] to our attention. CMB is supported by the U.S. Department of Energy. JF thanks the KITP at UC Santa Barbara for its hospitality while this paper was completed. His research at the KITP was supported in part by the National Science Foundation under Grant No. PHY05-51164. DWH is supported by Symplectic Ltd. DJW thanks the Imperial College High Performance Computing Service, URL: http: // www.imperial.ac.uk / ict/services / teachingandresearchservices/highperfor-mancecomputing.

PY - 2009/9

Y1 - 2009/9

N2 - This paper examines numerically the complex classical trajectories of the kicked rotor and the double pendulum. Both of these systems exhibit a transition to chaos, and this feature is studied in complex phase space. Additionally, it is shown that the short-time and long-time behaviours of these two PT -symmetric dynamical models in complex phase space exhibit strong qualitative similarities.

AB - This paper examines numerically the complex classical trajectories of the kicked rotor and the double pendulum. Both of these systems exhibit a transition to chaos, and this feature is studied in complex phase space. Additionally, it is shown that the short-time and long-time behaviours of these two PT -symmetric dynamical models in complex phase space exhibit strong qualitative similarities.

KW - Approach to chaos

KW - Double pendulum

KW - Kicked rotor

KW - PT symmetry

KW - Standard map

UR - http://www.scopus.com/inward/record.url?scp=70349559734&partnerID=8YFLogxK

U2 - 10.1007/s12043-009-0099-3

DO - 10.1007/s12043-009-0099-3

M3 - Article

AN - SCOPUS:70349559734

SN - 0304-4289

VL - 73

SP - 453

EP - 470

JO - Pramana - Journal of Physics

JF - Pramana - Journal of Physics

IS - 3

ER -

Chaotic systems in complex phase space

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this