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Abstract
It is well known that linear vector fields defined in Rn cannot have limit cycles, but this is not the case for linear vector fields defined in other manifolds. We study the existence of limit cycles bifurcating from a continuum of periodic orbits of linear vector fields on manifolds of the form (S2)m × Rn when such vector fields are perturbed inside the class of all linear vector fields. The study is done using averaging theory. We also present an open problem about the maximum number of limit cycles of linear vector fields on (S2)m × Rn.
| Original language | English |
|---|---|
| Pages (from-to) | 0249-263 |
| Number of pages | 15 |
| Journal | Pacific Journal of Mathematics |
| Volume | 324 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2023 |
Keywords
- Limit cycle
- Periodic orbit
- Isochronous center
- Averaging method
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Dive into the research topics of 'Limit cycles of linear vector fields on (S2)m ×Rn'. Together they form a unique fingerprint.Projects
- 2 Finished
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STUDY OF CONTINUOUS AND DISCRETE DYNAMIC SYSTEMS WITH EMPHASIS ON THEIR BIFURCATIONS, PERIODIC ORBITS AND INTEGRABILITY
Llibre Salo, J. (Principal Investigator), Torregrosa i Arús, J. (Co-Investigador/a Principal), Cufi Cabre, C. (Collaborator), Carvalho, Y. R. (Collaborator), Cousillas, G. (Collaborator), Diz Pita, É. (Collaborator), Ferragut Amengual, A. M. (Collaborator), GOUVEIA, L. F. D. S. (Collaborator), Iván Sánchez Sánchez (Collaborator), Jiménez Ruíz, J. J. (Collaborator), RODERO, A. L. (Collaborator), Ramírez, V. (Collaborator), Artes Ferragud, J. C. (Investigator), Caubergh , M. M. (Investigator), Cima Mollet, A. M. (Investigator), Corbera Subirana, M. (Investigator), Cors Iglesias, J. M. (Investigator), Gasull Embid, A. (Investigator), Pantazi ., C. (Investigator), Soler Villanueva, J. (Investigator), Garrido Pelaez, J. M. (Collaborator) & Valls Anglés, C. (Collaborator)
1/06/20 → 29/02/24
Project: Research Projects and Other Grants
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Algunos aspectos de la dinámica local y global de los sistemas dinámicos contínuos y discretos: Integrabilidad, Periodicidad y Bifurcaciones
Llibre Salo, J. (Principal Investigator), Torregrosa i Arús, J. (Co-Investigador/a Principal), Buzzi, C. A. (Collaborator), Candido , M. R. (Collaborator), Carvalho, Y. R. (Collaborator), Caubergh , M. M. (Collaborator), Cornelio, J. L. (Collaborator), Cousillas, G. (Collaborator), Cufi Cabre, C. (Collaborator), Diz Pita, É. (Collaborator), Ferragut Amengual, A. M. (Collaborator), Ferragut Amengual, A. (Collaborator), Geyer, A. (Collaborator), Giacomini, H. J. (Collaborator), Gouveia, L. F. (Collaborator), Jiménez Ruíz, J. J. (Collaborator), Lembarki, F. (Collaborator), Martínez, Y. P. (Collaborator), Pérez González, S. (Collaborator), Ramírez, V. (Collaborator), Saleta Reig, O. (Collaborator), Sanchez Sanchez, I. (Collaborator), Santos, R. A. T. (Collaborator), Schlomiuk, D. (Collaborator), Valls Angles, C. (Collaborator), Vulpe, N. (Collaborator), Zhang, X. (Collaborator), da Cruz, L. P. C. (Collaborator), de Almedia Silva Menezes, L. (Collaborator), Artes Ferragud, J. C. (Investigator), Caubergh , M. M. (Investigator), Cima Mollet, A. M. (Investigator), Corbera Subirana, M. (Investigator), Cors Iglesias, J. M. (Investigator), Gasull Embid, A. (Investigator), Pantazi, C. (Investigator) & Soler Villanueva, J. (Investigator)
Spanish Ministry of Economy and Competitiveness (MINECO)
30/12/16 → 31/12/20
Project: Research Projects and Other Grants