Hamiltonians with high-order integrals and the ‘‘weak-Painlevé’’ concept
- 1 December 1984
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 25 (12) , 3470-3473
- https://doi.org/10.1063/1.526103
Abstract
We examine the singularity structure of the equations of motion associated to integrable two-dimensional Hamiltonians with second integrals of order higher than 2. We show in these specific examples that the integrability is associated to a singularity expansion of the ‘‘weak-Painlevé’’ type. New cases of integrability are discovered, with still higher-order integrals which are explicitly computed.Keywords
This publication has 9 references indexed in Scilit:
- Explicit integrability for Hamiltonian systems and the Painlevé conjectureJournal of Mathematical Physics, 1984
- Integrability of Hamiltonians with third- and fourth-degree polynomial potentialsJournal of Mathematical Physics, 1983
- A new class of integrable systemsJournal of Mathematical Physics, 1983
- A theory of exact and approximate configurational invariantsPhysica D: Nonlinear Phenomena, 1983
- Painlevé Conjecture RevisitedPhysical Review Letters, 1982
- Construction of new integrable Hamiltonians in two degrees of freedomJournal of Mathematical Physics, 1982
- Painleve property and integrals of motion for the Henon-Heiles systemPhysics Letters A, 1982
- A connection between nonlinear evolution equations and ordinary differential equations of P-type. IJournal of Mathematical Physics, 1980
- Nonlinear evolution equations and ordinary differential equations of painlevè typeLettere al Nuovo Cimento (1971-1985), 1978