Advanced search
Publication Cover
Dynamical Systems
An International Journal
Volume 39, 2024 - Issue 2
Submit an article Journal homepage
47
Views
0
CrossRef citations to date
0
Altmetric
Research Article

On real center singularities of complex vector fields on surfaces

V. Leóna ILACVN -- CICN, Universidade Federal da Integração Latino-Americana, Parque tecnológico de Itaipu, Foz do IguaçuPR, BrazilCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0002-2082-6665
ORCID Icon &
B. Scárduab Instituto de Matemática -- Universidade Federal do Rio de Janeiro, Rio de JaneiroRJ, BrazilORCID Iconhttps://orcid.org/0000-0001-8280-1669
ORCID Icon
Pages 231-242 | Received 15 Mar 2023, Accepted 11 Oct 2023, Published online: 25 Oct 2023

References

  • M.S. Baouendi, P. Ebenfelt, and L.P. Rothschild, Real Submanifolds in Complex Space and Their Mappings, Princeton Mathematical Series; Vol. 47, Princeton University Press, Princeton, NJ, 1999.
  • M. Brunella and M. Villarini, On the poincaré-Lyapunov center theorem, Bol. Soc. Mat. Mex. (3) 5 (1999), pp. 155–161.
  • C. Camacho, On the local structure of conformal maps and holomorphic vector fields in C2, Astérisque 59(60) (1978), pp. 83–94. Jounées Singuliéres de Dijon (Univ. Dijon, Dijon, 1978, 3), Soc. Math. France, Paris.
  • C. Camacho and Lins Neto A., Geometric theory of foliations, Translated from the Portuguese by Sue E. Goodman. Birkhauser Boston, Inc., Boston, MA 1985.
  • C. Camacho and B. Scárdua, Nondicritical C∗-actions on two-dimensional Stein manifolds, Manuscripta Math. 129(1) (2009), pp. 91–98.
  • V. León and B. Scárdua, On a theorem of lyapunov-Poincaré in higher dimensions, Arnold Math. J. 7(4) (2021), pp. 561–571. https://doi.org/10.1007/s40598-021-00183-x.
  • A. Lyapunov, Etude d'un cas particulier du problème de la stabilité du mouvement, Mat. Sb. 17 (1893), pp. 252–333. (Russe).
  • J.F. Mattei and R. Moussu, Holonomie et intégrales premières, Ann. Sci. École Norm. Sup. 13(4) (1980), pp. 469–523.
  • R. Moussu, Une démonstration géométrique d'un théorème de Lyapunov-Poincaré, Astérisque 98(99) (1982), pp. 216–223. tome.
  • H. Poincaré, Mémoire sur les courbes définies par une équation différentielle (I), J. Math. Pures Appl. 7 (1881), pp. 375–422. 3e série, tome.
  • Roussarie Robert H., Bifurcation of Planar Vector Fields and Hilbert's Sixteenth Problem Volume 164 de Progress in Inflammation Research, Progress in mathematics; Vol. 164, Ed. Birkhäuser, 1998. ISSN 0743-1643.
  • M. Suzuki, Sur les opérations holomorphes de C et de C∗ sur un espace de Stein, Séminaire Norguet Springer Lect. Notes 670 (1977), pp. 80–88.
  • M. Suzuki, Sur les opérations holomorphes du groupe additif complexe sur l'espace de deux variables complexes, Ann. Sci. Éc. Norm. Sup. 10(4) (1977), pp. 517–546.
  • Urabe Minoru and Sibuya Yasutaka, On center of higher dimensions, J. Sci. Hiroshima Univ. Ser. A 19(1) (1955), pp. 87–100.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.