Dynamics and bifurcation near the transition from stability to complex instability: an analytical approach using normal forms
We consider a Hamiltonian of three degrees of freedom and a family of periodic orbits with a transition from stability to complex instability, such that there is an irrational collision of the Floquet eigenvalues of opposite sign. We analize the local dynamics and the bifurcation phenomena linked to...
| Autores: | ; ; |
|---|---|
| Tipo de documento: | Artigo |
| Data de publicação: | 1998 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositório: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | Inglês |
| OAI Identifier: | oai:upcommons.upc.edu:2117/1215 |
| Acesso em linha: | https://hdl.handle.net/2117/1215 |
| Nível de acesso: | Acesso aberto |
| Palavra-chave: | Hamiltonian dynamical systems Lagrangian functions Hamiltonian systems normal forms complex instability bifurcation Hamilton, Sistemes de Lagrange, Funcions de Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics |
| _version_ | 1878734190493564928 |
|---|---|
| author | Ollé Torner, Mercè|||0000-0002-8050-9055 |
| author2 | Pacha Andújar, Juan Ramón|||0000-0003-4599-3141 Villanueva Castelltort, Jordi|||0000-0001-8725-2785 |
| author2_role | author author |
| author_browse | Ollé Torner, Mercè|||0000-0002-8050-9055 Pacha Andújar, Juan Ramón|||0000-0003-4599-3141 Villanueva Castelltort, Jordi|||0000-0001-8725-2785 |
| author_facet | Ollé Torner, Mercè|||0000-0002-8050-9055 Pacha Andújar, Juan Ramón|||0000-0003-4599-3141 Villanueva Castelltort, Jordi|||0000-0001-8725-2785 |
| author_role | author |
| collection | UPCommons. Portal del coneixement obert de la UPC |
| description | We consider a Hamiltonian of three degrees of freedom and a family of periodic orbits with a transition from stability to complex instability, such that there is an irrational collision of the Floquet eigenvalues of opposite sign. We analize the local dynamics and the bifurcation phenomena linked to this transition. We study the resulting Hamiltonian Hopf-like bifurcation from an analy- tical point of view by means of normal forms. The existence of a bifurcating family of 2D tori is derived in both cases (direct and inverse bifur- cation) are described. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_65101d1ed09bdda675f01a2b775f20f9 |
| institution | Universitat Politècnica de Catalunya (UPC) |
| instname_str | Universitat Politècnica de Catalunya (UPC) |
| language | eng |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:upcommons.upc.edu:2117/1215 |
| publishDate | 1998 |
| publishDateSort | 1998 |
| reponame_str | UPCommons. Portal del coneixement obert de la UPC |
| spelling | Dynamics and bifurcation near the transition from stability to complex instability: an analytical approach using normal forms Ollé Torner, Mercè|||0000-0002-8050-9055 Pacha Andújar, Juan Ramón|||0000-0003-4599-3141 Villanueva Castelltort, Jordi|||0000-0001-8725-2785 Hamiltonian dynamical systems Lagrangian functions Hamiltonian systems normal forms complex instability bifurcation Hamilton, Sistemes de Lagrange, Funcions de Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics We consider a Hamiltonian of three degrees of freedom and a family of periodic orbits with a transition from stability to complex instability, such that there is an irrational collision of the Floquet eigenvalues of opposite sign. We analize the local dynamics and the bifurcation phenomena linked to this transition. We study the resulting Hamiltonian Hopf-like bifurcation from an analy- tical point of view by means of normal forms. The existence of a bifurcating family of 2D tori is derived in both cases (direct and inverse bifur- cation) are described. https://hdl.handle.net/2117/1215 |
| spellingShingle | Dynamics and bifurcation near the transition from stability to complex instability: an analytical approach using normal forms Ollé Torner, Mercè|||0000-0002-8050-9055 Hamiltonian dynamical systems Lagrangian functions Hamiltonian systems normal forms complex instability bifurcation Hamilton, Sistemes de Lagrange, Funcions de Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics |
| title | Dynamics and bifurcation near the transition from stability to complex instability: an analytical approach using normal forms |
| title_full | Dynamics and bifurcation near the transition from stability to complex instability: an analytical approach using normal forms |
| title_fullStr | Dynamics and bifurcation near the transition from stability to complex instability: an analytical approach using normal forms |
| title_full_unstemmed | Dynamics and bifurcation near the transition from stability to complex instability: an analytical approach using normal forms |
| title_short | Dynamics and bifurcation near the transition from stability to complex instability: an analytical approach using normal forms |
| title_sort | Dynamics and bifurcation near the transition from stability to complex instability: an analytical approach using normal forms |
| topic | Hamiltonian dynamical systems Lagrangian functions Hamiltonian systems normal forms complex instability bifurcation Hamilton, Sistemes de Lagrange, Funcions de Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics |
| topic_facet | Hamiltonian dynamical systems Lagrangian functions Hamiltonian systems normal forms complex instability bifurcation Hamilton, Sistemes de Lagrange, Funcions de Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics |
| url | https://hdl.handle.net/2117/1215 |