Journal of Nonlinear Mathematical Physics

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Volume 12, Issue Supplement 1, January 2005, Pages 212 - 227

Explicit integration of the Hénon-Heiles Hamiltonians 1

Authors
Robert Conte, Micheline Musette, Caroline Verhoeven
Corresponding Author
Robert Conte
Available Online 1 January 2005.
DOI
10.2991/jnmp.2005.12.s1.18How to use a DOI?
Abstract

We consider the cubic and quartic Hénon-Heiles Hamiltonians with additional inverse square terms, which pass the Painlevé test for only seven sets of coefficients. For all the not yet integrated cases we prove the singlevaluedness of the general solution. The seven Hamiltonians enjoy two properties: meromorphy of the general solution, which is hyperelliptic with genus two and completeness in the Painlevé sense (impossibility to add any term to the Hamiltonian without destroying the Painlevé property).

Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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<Previous Article In Issue
Next Article In Issue>
Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
12 - Supplement 1
Pages
212 - 227
Publication Date
2005/01/01
ISBN
91-974824-3-9
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.2005.12.s1.18How to use a DOI?
Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Robert Conte
AU  - Micheline Musette
AU  - Caroline Verhoeven
PY  - 2005
DA  - 2005/01/01
TI  - Explicit integration of the Hénon-Heiles Hamiltonians 1
JO  - Journal of Nonlinear Mathematical Physics
SP  - 212
EP  - 227
VL  - 12
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2005.12.s1.18
DO  - 10.2991/jnmp.2005.12.s1.18
ID  - Conte2005
ER  -