Publication: Reeb’s theorem and periodic orbits for a rotating Hénon–Heiles potential
Consultable a partir de
2020-12-04
Date
2019
Authors
Lanchares, Víctor
Pascual, Ana Isabel
Iñarrea, Manuel
Salas, José Pablo
Palacián Subiela, Jesús Francisco
Director
Publisher
Springer
Acceso abierto / Sarbide irekia
Artículo / Artikulua
Versión aceptada / Onetsi den bertsioa
Project identifier
MINECO//MTM2014-59433-C2-1-P/ES/
AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-88137-C2-1-P/ES/
AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-88137-C2-1-P/ES/
Abstract
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.
Keywords
Averaging, Normalization, Reduced space, Hamiltonian oscillators, Periodic solutions
Department
Estatistika, Informatika eta Matematika / Institute for Advanced Materials and Mathematics - INAMAT2 / Estadística, Informática y Matemáticas
Faculty/School
Degree
Doctorate program
Editor version
Funding entities
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.
© Springer Science+Business Media, LLC, part of Springer Nature 2019
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