The first part of the paper is devoted to the theory of master symmetries using the geometric formalism as an approach. It is shown that certain superintegrable systems are endowed with this property as a consequence of the existence of a family of master symmetries. In the second part, the properties of dynamical but non-Hamiltonian symmetries are studied. It is proved that the higher order superintegrability of the generalized Smorodinsky-Winternitz system is a consequence of the existence of symplectic symmetries not preserving the Hamiltonian function.
机构:
Zhejiang Normal Univ, Coll Math Sci, Jinhua 321004, Peoples R ChinaZhejiang Normal Univ, Coll Math Sci, Jinhua 321004, Peoples R China
Fan, Zhiping
Zhang, Duanzhi
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机构:
Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China
Nankai Univ, LPMC, Tianjin 300071, Peoples R ChinaZhejiang Normal Univ, Coll Math Sci, Jinhua 321004, Peoples R China