04984nam 2200673Ia 450 991078227560332120230607222206.01-281-94825-X9786611948252981-279-855-2(CKB)1000000000538121(EBL)1679746(OCoLC)879074291(SSID)ssj0000201998(PQKBManifestationID)11179684(PQKBTitleCode)TC0000201998(PQKBWorkID)10253069(PQKB)11750250(MiAaPQ)EBC1679746(WSP)00004221(Au-PeEL)EBL1679746(CaPaEBR)ebr10255836(EXLCZ)99100000000053812120020111d2001 uy 0engur|n|---|||||txtccrMethods of qualitative theory in nonlinear dynamicsPart II[electronic resource] /Leonid P. Shilnikov ... [et al.]Singapore ;River Edge, NJ World Scientific20011 online resource (591 p.)World scientific series on nonlinear science. Series A, Monographs and treatises ;5Description based upon print version of record.981-02-4072-4 Includes bibliographical references and indexes.Contents ; 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 systems7.5. 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 systems8.3. 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 STATES9.1. 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 functions10.2. 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 resonancesChapter 11. LOCAL BIFURCATIONS ON THE ROUTE OVER STABILITY BOUNDARIES 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 Poincaré, and the renowned Andronov school of nonlinear oscillations, this book focuses on the <i>qualitative</i> study of <i>high-dimensional</i> nonlinear dynamicalWorld Scientific Series on Nonlinear Science Series ANonlinear theoriesNonlinear mechanicsNonlinear theories.Nonlinear mechanics.514.74514/.74620.10401515355Shilʹnikov L. P54739MiAaPQMiAaPQMiAaPQBOOK9910782275603321Methods of qualitative theory in nonlinear dynamics3719590UNINA