Analytic structure of the Henon-Heiles Hamiltonian in integrable and nonintegrable regimes

Y. F. Chang, Michael Tabor, J. Weiss

Research output: Contribution to journalArticle

177 Citations (Scopus)

Abstract

The solutions of the Henon-Heiles Hamiltonian are investigated in the complex time plane. The use of the "Painlevé property," i.e., the property that the only movable singularities exhibited by the solution are poles, enables successful prediction of the values of the nonlinear coupling parameter for which the system is integrable. Special attention is paid to the structure of the natural boundaries that are found in some of the nonintegrable regimes. These boundaries have a remarkable self-similar structure whose form changes as a function of the nonlinear coupling.

Original languageEnglish (US)
Pages (from-to)531-538
Number of pages8
JournalJournal of Mathematical Physics
Volume23
Issue number4
StatePublished - 1981
Externally publishedYes

Fingerprint

Hamiltonians
Pole
Poles
poles
Singularity
Prediction
predictions
Form

ASJC Scopus subject areas

  • Organic Chemistry

Cite this

Analytic structure of the Henon-Heiles Hamiltonian in integrable and nonintegrable regimes. / Chang, Y. F.; Tabor, Michael; Weiss, J.

In: Journal of Mathematical Physics, Vol. 23, No. 4, 1981, p. 531-538.

Research output: Contribution to journalArticle

@article{4d7bea5920084ac0bbf2857e59be05b3,
title = "Analytic structure of the Henon-Heiles Hamiltonian in integrable and nonintegrable regimes",
abstract = "The solutions of the Henon-Heiles Hamiltonian are investigated in the complex time plane. The use of the {"}Painlev{\'e} property,{"} i.e., the property that the only movable singularities exhibited by the solution are poles, enables successful prediction of the values of the nonlinear coupling parameter for which the system is integrable. Special attention is paid to the structure of the natural boundaries that are found in some of the nonintegrable regimes. These boundaries have a remarkable self-similar structure whose form changes as a function of the nonlinear coupling.",
author = "Chang, {Y. F.} and Michael Tabor and J. Weiss",
year = "1981",
language = "English (US)",
volume = "23",
pages = "531--538",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "American Institute of Physics Publising LLC",
number = "4",

}

TY - JOUR

T1 - Analytic structure of the Henon-Heiles Hamiltonian in integrable and nonintegrable regimes

AU - Chang, Y. F.

AU - Tabor, Michael

AU - Weiss, J.

PY - 1981

Y1 - 1981

N2 - The solutions of the Henon-Heiles Hamiltonian are investigated in the complex time plane. The use of the "Painlevé property," i.e., the property that the only movable singularities exhibited by the solution are poles, enables successful prediction of the values of the nonlinear coupling parameter for which the system is integrable. Special attention is paid to the structure of the natural boundaries that are found in some of the nonintegrable regimes. These boundaries have a remarkable self-similar structure whose form changes as a function of the nonlinear coupling.

AB - The solutions of the Henon-Heiles Hamiltonian are investigated in the complex time plane. The use of the "Painlevé property," i.e., the property that the only movable singularities exhibited by the solution are poles, enables successful prediction of the values of the nonlinear coupling parameter for which the system is integrable. Special attention is paid to the structure of the natural boundaries that are found in some of the nonintegrable regimes. These boundaries have a remarkable self-similar structure whose form changes as a function of the nonlinear coupling.

UR - http://www.scopus.com/inward/record.url?scp=36749106140&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36749106140&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:36749106140

VL - 23

SP - 531

EP - 538

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 4

ER -