Reeb’s theorem and periodic orbits for a rotating Hénon–Heiles potential
Fecha
2019Autor
Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión aceptada / Onetsi den bertsioa
Identificador del proyecto
Impacto
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10.1007/s10884-019-09814-6
Resumen
We apply Reeb’s theorem to prove the existence of periodic orbits in the rotating Hénon–
Heiles system. To this end, a sort of detuned normal form is calculated that yields a reduced
system with at most four non degenerate equilibrium points. Linear stability and bifurcations
of equilibrium solutions mimic those for periodic solutions of the original system. We also
determine heteroclinic con ...
[++]
We apply Reeb’s theorem to prove the existence of periodic orbits in the rotating Hénon–
Heiles system. To this end, a sort of detuned normal form is calculated that yields a reduced
system with at most four non degenerate equilibrium points. Linear stability and bifurcations
of equilibrium solutions mimic those for periodic solutions of the original system. We also
determine heteroclinic connections that can account for transport phenomena. [--]
Materias
Averaging,
Normalization,
Reduced space,
Hamiltonian oscillators,
Periodic solutions
Editor
Springer
Publicado en
Journal of Dynamics and Differential Equations (2019)
Departamento
Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas /
Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila /
Universidad Pública de Navarra/Nafarroako Unibertsitate Publikoa. Institute for Advanced Materials and Mathematics - INAMAT2
Versión del editor
Entidades Financiadoras
This work has been partly supported from the Spanish Ministry of Science and Innovation
through the Projects MTM2014-59433-CO (Subprojects MTM2014-59433-C2-1-P and MTM2014-59433-
C2-2-P), MTM2017-88137-CO (Subprojects MTM2017-88137-C2-1-P and MTM2017-88137-C2-2-P), and
by University of La Rioja through Project REGI 2018751.