03278nam 22005175 450 991025428120332120251116172236.0981-10-4226-810.1007/978-981-10-4226-3(CKB)3710000001127306(DE-He213)978-981-10-4226-3(MiAaPQ)EBC4833997(PPN)199764727(EXLCZ)99371000000112730620170330d2017 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierIntegrability of dynamical systems: algebra and analysis /by Xiang Zhang1st ed. 2017.Singapore :Springer Singapore :Imprint: Springer,2017.1 online resource (XV, 380 p. 6 illus., 1 illus. in color.)Developments in Mathematics,1389-2177 ;47981-10-4225-X The fundamentals of the theory of integrability of differential systems -- The fundamentals of the theory of integrability of differential systems -- The fundamentals of the theory of integrability of differential systems -- Existence and degree of Darboux polynomials -- Algebraic, analytic and meromorphic integrability -- Applications of the Darboux theory of integrability -- Local integrability of differential systems -- Index.This is the first book to systematically state the fundamental theory of integrability and its development of ordinary differential equations with emphasis on the Darboux theory of integrability and local integrability together with their applications. It summarizes the classical results of Darboux integrability and its modern development together with their related Darboux polynomials and their applications in the reduction of Liouville and elementary integrabilty and in the center—focus problem, the weakened Hilbert 16th problem on algebraic limit cycles and the global dynamical analysis of some realistic models in fields such as physics, mechanics and biology.    Although it can be used as a textbook for graduate students in dynamical systems, it is intended as supplementary reading for graduate students from mathematics, physics, mechanics and engineering in courses related to the qualitative theory, bifurcation theory and the theory of integrability of dynamical systems.Developments in Mathematics,1389-2177 ;47Differential equationsStatistical physicsOrdinary Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12147Applications of Nonlinear Dynamics and Chaos Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/P33020Differential equations.Statistical physics.Ordinary Differential Equations.Applications of Nonlinear Dynamics and Chaos Theory.515.352Zhang Xiangauthttp://id.loc.gov/vocabulary/relators/aut651555MiAaPQMiAaPQMiAaPQBOOK9910254281203321Integrability of dynamical systems1560434UNINA