Integrability of complex planar systems with homogeneous nonlinearities

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:434

Article

Fercec, Brigita^1,2  Gine, Jaume³  Romanovski, Valery G.^2,4  Edneral, Victor F.^5,6 

[1] Univ Maribor, Fac Energy Technol, SI-8270 Krshko, Slovenia

[2] Univ Maribor, Ctr Appl Math & Theoret Phys, SI-2000 Maribor, Slovenia

[3] Univ Lleida, Dept Matemat, Lleida 25001, Catalonia, Spain

[4] Univ Maribor, Fac Nat Sci & Math, SI-2000 Maribor, Slovenia

[5] Lomonosov Moscow State Univ SINP MSU, Skobeltsyn Inst Nucl Phys, Moscow 119991, Russia

[6] PFUR, Fac Phys Math & Nat Sci, Moscow 117198, Russia

关键词: Integrability;    Center problem;    Time-reversibility;   

DOI  :  10.1016/j.jmaa.2015.09.037

来源: Elsevier

【 摘 要 】

In this paper we obtain sufficient conditions for the existence of a local analytic first integral for a family of quintic systems having homogeneous nonlinearities. The family studied in this work is the largest one classified until now for systems with such nonlinearities. We propose also an approach to find reversible systems within polynomial families of Lotka-Volterra systems with homogeneous nonlinearities. (C) 2015 Published by Elsevier Inc.

【 授权许可】

Free