Quasi-bi-Hamiltonian structures and superintegrability: Study of a Kepler-related family of systems endowed with generalized Runge-Lenz integrals of motion

Fernández Rañada, M. (Universidad de Zaragoza)

Resumen: The existence of quasi-bi-Hamiltonian structures for a two-dimensional superintegrable (k(1), k(2), k(3))-dependent Kepler-related problem is studied. We make use of an approach that is related with the existence of some complex functions which satisfy interesting Poisson bracket relations and that was previously applied to the standard Kepler problem as well as to some particular superintegrable systems as the Smorodinsky-Winternitz (SW) system, the Tremblay-Turbiner-Winternitz (TTW) and Post-Winternitz (PW) systems. We prove that these complex functions are important for two reasons: first, they determine the integrals of motion, and second they determine the existence of some geometric structures (in this particular case, quasi-bi-Hamiltonian structures). All the results depend on three parameters (k(1), k(2), k(3)) in such a way that in the particular case k(1) not equal 0, k(2) = k(3) = 0, the properties characterizing the Kepler problem are obtained. This paper can be considered as divided in two parts and every part presents a different approach (different complex functions and different quasi-bi-Hamiltonian structures).

Idioma: Inglés

DOI: 10.3934/jgm.2021003

Año: 2021

Publicado en: JOURNAL OF GEOMETRIC MECHANICS 13, 2 (2021), 195-208
ISSN: 1941-4889

Factor impacto JCR: 0.737 (2021)

Categ. JCR: PHYSICS, MATHEMATICAL rank: 50 / 56 = 0.893 (2021) - Q4 - T3
Categ. JCR: MATHEMATICS, APPLIED rank: 232 / 267 = 0.869 (2021) - Q4 - T3

Factor impacto CITESCORE: 1.3 - Mathematics (Q3) - Engineering (Q3)

Factor impacto SCIMAGO: 0.26 - Applied Mathematics (Q3) - Mechanics of Materials (Q3) - Geometry and Topology (Q3)

Tipo y forma: Article (PostPrint)

Área (Departamento): Área Física Teórica (Dpto. Física Teórica)