LEADER 03245nam 2200601 a 450 001 9910438142603321 005 20200520144314.0 010 $a1-299-19770-1 010 $a3-642-33817-8 024 7 $a10.1007/978-3-642-33817-5 035 $a(CKB)2670000000328003 035 $a(EBL)1082733 035 $a(OCoLC)826853744 035 $a(SSID)ssj0000878491 035 $a(PQKBManifestationID)11482768 035 $a(PQKBTitleCode)TC0000878491 035 $a(PQKBWorkID)10832356 035 $a(PQKB)11233085 035 $a(DE-He213)978-3-642-33817-5 035 $a(MiAaPQ)EBC1082733 035 $a(PPN)168325489 035 $a(EXLCZ)992670000000328003 100 $a20130130d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAsymptotic solutions of strongly nonlinear systems of differential equations /$fValery V. Kozlov, Stanislav D. Furta 205 $a1st ed. 2013. 210 $aBerlin $cSpringer$d2013 215 $a1 online resource (277 p.) 225 0$aSpringer monographs in mathematics,$x1439-7382 300 $aDescription based upon print version of record. 311 $a3-642-43240-9 311 $a3-642-33816-X 320 $aIncludes bibliographical references and index. 327 $aPreface -- 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. 330 $aThe book is dedicated to the construction of particular solutions of systems of ordinary differential equations in the form of series that are analogous to those used in Lyapunov?s first method. A prominent place is given to asymptotic solutions that tend to an equilibrium position, especially in the strongly nonlinear case, where the existence of such solutions can?t be inferred on the basis of the first approximation alone. The book is illustrated with a large number of concrete examples of systems in which the presence of a particular solution of a certain class is related to special properties of the system?s dynamic behavior. It is a book for students and specialists who work with dynamical systems in the fields of mechanics, mathematics, and theoretical physics. 410 0$aSpringer Monographs in Mathematics,$x1439-7382 606 $aDifferential equations$xAsymptotic theory 615 0$aDifferential equations$xAsymptotic theory. 676 $a515 676 $a515/.3535 700 $aKozlov$b V. V$g(Valerii Viktorovich)$059678 701 $aFurta$b Stanislav D$01758819 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438142603321 996 $aAsymptotic solutions of strongly nonlinear systems of differential equations$94197067 997 $aUNINA