Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 11 (2015), 094, 9 pages      arXiv:1509.07288
Contribution to the Special Issue on Analytical Mechanics and Differential Geometry in honour of Sergio Benenti

Extended Hamiltonians, Coupling-Constant Metamorphosis and the Post-Winternitz System

Claudia Maria Chanu, Luca Degiovanni and Giovanni Rastelli
Dipartimento di Matematica, Università di Torino, Torino, via Carlo Alberto 10, Italy

Received September 26, 2015, in final form November 16, 2015; Published online November 24, 2015

The coupling-constant metamorphosis is applied to modified extended Hamiltonians and sufficient conditions are found in order that the transformed high-degree first integral of the transformed Hamiltonian is determined by the same algorithm which computes the corresponding first integral of the original extended Hamiltonian. As examples, we consider the Post-Winternitz system and the 2D caged anisotropic oscillator.

Key words: superintegrable systems; extended systems; coupling-constant metamorphosis.

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