Dynamics, integrability and topology for Lotka-Volterra Hamiltonian systems in R^4
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Xiao, Dongmei (Shanghai Jiao Tong University. School of Mathematical Sciences)

Date:	2017
Abstract:	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.
Grants:	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
Note:	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).
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Darboux first integral ; Dynamics ; Hamiltonian system ; Kolmogorov system ; Liouvillian integrability
Published in:	Journal of differential equations, Vol. 262 Núm. 3 (2017) , p. 2231-2253, ISSN 1090-2732

DOI: 10.1016/j.jde.2016.10.042

Postprint 22 p, 505.3 KB

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