LEADER 05018nam 2200685Ia 450 001 9910453553603321 005 20200520144314.0 010 $a1-281-94825-X 010 $a9786611948252 010 $a981-279-855-2 035 $a(CKB)1000000000538121 035 $a(EBL)1679746 035 $a(OCoLC)879074291 035 $a(SSID)ssj0000201998 035 $a(PQKBManifestationID)11179684 035 $a(PQKBTitleCode)TC0000201998 035 $a(PQKBWorkID)10253069 035 $a(PQKB)11750250 035 $a(MiAaPQ)EBC1679746 035 $a(WSP)00004221 035 $a(Au-PeEL)EBL1679746 035 $a(CaPaEBR)ebr10255836 035 $a(EXLCZ)991000000000538121 100 $a20020111d2001 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aMethods of qualitative theory in nonlinear dynamics$hPart II$b[electronic resource] /$fLeonid P. Shilnikov ... [et al.] 210 $aSingapore ;$aRiver Edge, NJ $cWorld Scientific$d2001 215 $a1 online resource (591 p.) 225 0 $aWorld scientific series on nonlinear science. Series A, Monographs and treatises ;$v5 300 $aDescription based upon print version of record. 311 $a981-02-4072-4 320 $aIncludes bibliographical references and indexes. 327 $aContents ; Introduction to Part II ; Chapter 7. STRUCTURALLY STABLE SYSTEMS ; 7.1. Rough systems on a plane. Andronov-Pontryagin theorem ; 7.2. The set of center motions ; 7.3. General classification of center motions ; 7.4. Remarks on roughness of high-order dynamical systems 327 $a7.5. Morse-Smale systems 7.6. Some properties of Morse-Smale systems ; Chapter 8. BIFURCATIONS OF DYNAMICAL SYSTEMS ; 8.1. Systems of first degree of non-roughness ; 8.2. Remarks on bifurcations of multi-dimensional systems 327 $a8.3. Structurally unstable homoclinic and heteroclinic orbits. Moduli of topological equivalence 8.4. Bifurcations in finite-parameter families of systems. Andronov's setup ; Chapter 9. THE BEHAVIOR OF DYNAMICAL SYSTEMS ON STABILITY BOUNDARIES OF EQUILIBRIUM STATES 327 $a9.1. The reduction theorems. The Lyapunov functions 9.2. The first critical case ; 9.3. The second critical case ; Chapter 10. THE BEHAVIOR OF DYNAMICAL SYSTEMS ON STABILITY BOUNDARIES OF PERIODIC TRAJECTORIES ; 10.1. The reduction of the Poincare map. Lyapunov functions 327 $a10.2. The first critical case 10.3. The second critical case ; 10.4. The third critical case. Weak resonances ; 10.5. Strong resonances ; 10.6. Passage through strong resonance on stability boundary ; 10.7. Additional remarks on resonances 327 $aChapter 11. LOCAL BIFURCATIONS ON THE ROUTE OVER STABILITY BOUNDARIES 330 $a Bifurcation and chaos has dominated research in nonlinear dynamics for over two decades, and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book has been written to serve that unfulfilled need. Following the footsteps of Poincare?, and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical 410 0$aWorld Scientific Series on Nonlinear Science Series A 606 $aNonlinear theories 606 $aNonlinear mechanics 608 $aElectronic books. 615 0$aNonlinear theories. 615 0$aNonlinear mechanics. 676 $a514.74 676 $a514/.74 676 $a620.10401515355 701 $aShil?nikov$b L. P$054739 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910453553603321 996 $aMethods of qualitative theory in nonlinear dynamics$92265288 997 $aUNINA