• Corpus ID: 117451861

Painleve' property of the He'non-Heiles Hamiltonians

@article{Conte2006PainlevePO,
  title={Painleve' property of the He'non-Heiles Hamiltonians},
  author={R. Conte and Micheline Musette and Caroline Verhoeven},
  journal={arXiv: Exactly Solvable and Integrable Systems},
  year={2006}
}
Time independent Hamiltonians of the physical type H = (P_1^2+P_2^2)/2+V(Q_1,Q_2) pass the Painleve' test for only seven potentials $V$, known as the He'non-Heiles Hamiltonians, each depending on a finite number of free constants. Proving the Painleve' property was not yet achieved for generic values of the free constants. We integrate each missing case by building a birational transformation to some fourth order first degree ordinary differential equation in the classification (Cosgrove, 2000… 
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The quartic Henon-Heiles Hamiltonian passes the Painleve test for only four sets of values of the constants. Only one of these, identical to the traveling-wave reduction of the Manakov system, has…
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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…
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