Master symmetries, non-Hamiltonian symmetries and superintegrability of the generalized Smorodinsky-Winternitz system (Q2881348)

In this paper superintegrability properties are studied and their relation to the existence of master symmetries and non-Hamilton symmetries are analyzed. The first part of the paper is devoted to the theory of master symmetries using the geometric formalism. 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.NEWLINENEWLINE This work consists of the following parts: Introduction; Master symmetries and superintegrability, four particular simple cases, differential geometric approach, a new look to the previous examples; Non-Hamiltonian symmetries and superintegrability, higher order superintegribility of the generalized Smorodinsky-Winternitz system; Final comments.