03245nam 2200601 a 450 991043814260332120200520144314.01-299-19770-13-642-33817-810.1007/978-3-642-33817-5(CKB)2670000000328003(EBL)1082733(OCoLC)826853744(SSID)ssj0000878491(PQKBManifestationID)11482768(PQKBTitleCode)TC0000878491(PQKBWorkID)10832356(PQKB)11233085(DE-He213)978-3-642-33817-5(MiAaPQ)EBC1082733(PPN)168325489(EXLCZ)99267000000032800320130130d2013 uy 0engur|n|---|||||txtccrAsymptotic solutions of strongly nonlinear systems of differential equations /Valery V. Kozlov, Stanislav D. Furta1st ed. 2013.Berlin Springer20131 online resource (277 p.)Springer monographs in mathematics,1439-7382Description based upon print version of record.3-642-43240-9 3-642-33816-X Includes bibliographical references and index.Preface -- Semi-quasihomogeneous systems of ordinary differential equations -- 2. The critical case of purely imaginary kernels -- 3. Singular problems -- 4. The inverse problem for the Lagrange theorem on the stability of equilibrium and other related problems -- Appendix A. Nonexponential asymptotic solutions of systems of functional-differential equations -- Appendix B. Arithmetic properties of the eigenvalues of the Kovalevsky matrix and conditions for the nonintegrability of semi-quasihomogeneous systems of ordinary dierential equations -- Bibliography.The book is dedicated to the construction of particular solutions of systems of ordinary differential equations in the form of series that are analogous to those used in Lyapunov’s first method. A prominent place is given to asymptotic solutions that tend to an equilibrium position, especially in the strongly nonlinear case, where the existence of such solutions can’t be inferred on the basis of the first approximation alone. The book is illustrated with a large number of concrete examples of systems in which the presence of a particular solution of a certain class is related to special properties of the system’s dynamic behavior. It is a book for students and specialists who work with dynamical systems in the fields of mechanics, mathematics, and theoretical physics.Springer Monographs in Mathematics,1439-7382Differential equationsAsymptotic theoryDifferential equationsAsymptotic theory.515515/.3535Kozlov V. V(Valerii Viktorovich)59678Furta Stanislav D1758819MiAaPQMiAaPQMiAaPQBOOK9910438142603321Asymptotic solutions of strongly nonlinear systems of differential equations4197067UNINA