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- W2727593374 abstract "The existence of quasi-bi-Hamiltonian structures for the Tremblay–Turbiner–Winternitz (TTW) and the Post–Winternitz (PW) systems is studied. We first recall that the superintegrability of these two systems is related with the existence of certain complex functions endowed with interesting Poisson bracket properties, and then we prove the existence of several quasi-bi-Hamiltonian structures making use of these complex functions. This is done in two steps: first with complex 2-forms (wedge product of the differentials of the complex functions) and then with several real 2-forms. The properties of these geometric structures and the associated recursion operators are also analyzed. The paper can be considered as divided in two parts. In the first part a we study the TTW system (related to the harmonic oscillator) and in the second part we study the PW system (related to the Kepler problem)." @default.
- W2727593374 created "2017-07-14" @default.
- W2727593374 creator A5026547458 @default.
- W2727593374 date "2017-07-07" @default.
- W2727593374 modified "2023-10-16" @default.
- W2727593374 title "Quasi-bi-Hamiltonian structures, complex functions and superintegrability: the Tremblay–Turbiner–Winternitz (TTW) and the Post–Winternitz (PW) systems" @default.
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- W2727593374 doi "https://doi.org/10.1088/1751-8121/aa7951" @default.
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