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Página principal > Artículos > Artículos publicados > Dynamics, integrability and topology for Lotka-Volterra Hamiltonian systems in R^4 |
Fecha: | 2017 |
Resumen: | In this paper first we give the sufficient and necessary conditions in order that two classes of polynomial Kolmogorov systems in \R_ ^4 are Hamiltonian systems. After we study the integrability of these Hamiltonian systems in the Liouville sense. Finally, we investigate the global dynamics of the completely integrable Lotka--Volterra Hamiltonian systems in \R_ ^4. As an application of the invariant subsets of these systems, we obtain topological classifications of the 3-submanifolds in \R_ ^4 defined by the hypersurfaces a x y b z w c x^2 y d x y^2 e z^2 w f z w^2= constant. |
Ayudas: | Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 316338 European Commission 318999 Ministerio de Economía y Competitividad MTM2013-40998-P Ministerio de Economía y Competitividad MTM2016-77278-P |
Nota: | Agraïments: The second author is partially supported by the National Natural Science Foundation of China (No. 11371248 & No. 11431008) and the RFDP of Higher Education of China grant (No. 20130073110074). |
Derechos: | Tots els drets reservats. |
Lengua: | Anglès |
Documento: | Article ; recerca ; Versió acceptada per publicar |
Materia: | Darboux first integral ; Dynamics ; Hamiltonian system ; Kolmogorov system ; Liouvillian integrability |
Publicado en: | Journal of differential equations, Vol. 262 Núm. 3 (2017) , p. 2231-2253, ISSN 1090-2732 |
Postprint 22 p, 505.3 KB |