### Abstract

For an n degree of freedom hyperelliptic separable hamiltonian, the pole series with n+1 free constants, through the Hamilton-Jacobi equation, bounds the degrees of the n-polynomials in involution. When all the pole series have no fewer than 2n constants, the phase space is conjectured to be just the direct product of 2n complex lines cut out by (2n-1) integrals.

Original language | English (US) |
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Pages (from-to) | 112-116 |

Number of pages | 5 |

Journal | Physics Letters A |

Volume | 119 |

Issue number | 3 |

DOIs | |

State | Published - Dec 8 1986 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physics Letters A*,

*119*(3), 112-116. https://doi.org/10.1016/0375-9601(86)90426-3

**Painlevé property and integrability.** / Ercolani, Nicholas M; Siggia, Eric D.

Research output: Contribution to journal › Article

*Physics Letters A*, vol. 119, no. 3, pp. 112-116. https://doi.org/10.1016/0375-9601(86)90426-3

}

TY - JOUR

T1 - Painlevé property and integrability

AU - Ercolani, Nicholas M

AU - Siggia, Eric D.

PY - 1986/12/8

Y1 - 1986/12/8

N2 - For an n degree of freedom hyperelliptic separable hamiltonian, the pole series with n+1 free constants, through the Hamilton-Jacobi equation, bounds the degrees of the n-polynomials in involution. When all the pole series have no fewer than 2n constants, the phase space is conjectured to be just the direct product of 2n complex lines cut out by (2n-1) integrals.

AB - For an n degree of freedom hyperelliptic separable hamiltonian, the pole series with n+1 free constants, through the Hamilton-Jacobi equation, bounds the degrees of the n-polynomials in involution. When all the pole series have no fewer than 2n constants, the phase space is conjectured to be just the direct product of 2n complex lines cut out by (2n-1) integrals.

UR - http://www.scopus.com/inward/record.url?scp=0010054584&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0010054584&partnerID=8YFLogxK

U2 - 10.1016/0375-9601(86)90426-3

DO - 10.1016/0375-9601(86)90426-3

M3 - Article

VL - 119

SP - 112

EP - 116

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 3

ER -