Reeb’s theorem and periodic orbits for a rotating Hénon–Heiles potential

Date

2019

Authors

Lanchares, Víctor
Pascual, Ana Isabel
Iñarrea, Manuel
Salas, José Pablo

Director

Publisher

Springer
Acceso abierto / Sarbide irekia
Artículo / Artikulua
Versión aceptada / Onetsi den bertsioa

Project identifier

  • MINECO//MTM2014-59433-C2-1-P/ES/ recolecta
  • AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-88137-C2-1-P/ES/ recolecta
Impacto

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.

Description

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

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