Reeb’s Theorem and Periodic Orbits for a Rotating Hénon–Heiles Potential
| Autor: | Víctor Lanchares, Ana I. Pascual, Jesús F. Palacián, J. P. Salas, Manuel Iñarrea, Patricia Yanguas |
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| Přispěvatelé: | Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas, Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa. INAMAT2 - Institute for Advanced Materials and Mathematics, Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila, Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa. InaMat - Institute for Advanced Materials |
| Rok vydání: | 2019 |
| Předmět: |
Equilibrium point
Normalization (statistics) Partial differential equation Periodic solutions 010102 general mathematics Mathematical analysis Degenerate energy levels 01 natural sciences Reduced space Nonlinear Sciences::Chaotic Dynamics 010101 applied mathematics Normalization Averaging Ordinary differential equation Hamiltonian oscillators sort 0101 mathematics Transport phenomena Analysis Mathematics Linear stability |
| Zdroj: | Academica-e. Repositorio Institucional de la Universidad Pública de Navarra instname Academica-e: Repositorio Institucional de la Universidad Pública de Navarra Universidad Pública de Navarra |
| ISSN: | 1572-9222 1040-7294 |
| DOI: | 10.1007/s10884-019-09814-6 |
| Popis: | 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. 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. |
| Databáze: | OpenAIRE |
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