Energy dependent integrability

JOURNAL OF GEOMETRY AND PHYSICS

卷:115

Article

Pucacco, Giuseppe^1,2  Rosquist, Kjell³ 

[1] Univ Roma Tor Vergata, Dipartimento Fis, Via Ric Sci 1, I-00133 Rome, Italy

[2] Univ Roma Tor Vergata, Ist Nazl Fis Nucl, Sez Roma 2, Via Ric Sci 1, I-00133 Rome, Italy

[3] Stockholm Univ, Dept Phys, S-10691 Stockholm, Sweden

关键词: Finite-dimensional Hamiltonian systems;    Completely Integrable Systems;    Symmetries and conservation laws;   

DOI  :  10.1016/j.geomphys.2016.10.001

来源: Elsevier

【 摘 要 】

We review the conditions for separability of 2-dimensional natural Hamiltonian systems. We examine the possibility that the separability condition is satisfied on a given energy hypersurface only (weak integrability) and derive the additional requirement necessary to have separability at arbitrary values of the Hamiltonian (strong integrability). We give some new examples of systems admitting separating coordinates whose relation with the original ones explicitly depends on energy and provide a list of separable potentials discussing the nature of conserved quantities they admit. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free