LEADER 03502nam 22006375 450 001 9910739408003321 005 20251009082229.0 010 $a3-031-33046-3 024 7 $a10.1007/978-3-031-33046-9 035 $a(CKB)27983580600041 035 $a(DE-He213)978-3-031-33046-9 035 $a(MiAaPQ)EBC30766889 035 $a(Au-PeEL)EBL30766889 035 $a(PPN)272260991 035 $a(MiAaPQ)EBC30684856 035 $a(Au-PeEL)EBL30684856 035 $a(EXLCZ)9927983580600041 100 $a20230811d2023 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNormal Forms and Stability of Hamiltonian Systems /$fby Hildeberto E. Cabral, Lúcia Brandăo Dias 205 $a1st ed. 2023. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2023. 215 $a1 online resource (XXI, 337 p. 29 illus., 13 illus. in color.) 225 1 $aApplied Mathematical Sciences,$x2196-968X ;$v218 311 08$a9783031330452 320 $aIncludes bibliographical references and index. 327 $aForeword -- Preliminaries on Advanced Calculus -- Hamiltonian Systems Theory -- Normal Forms of Hamiltonian Systems -- Spectral Decomposition of Hamiltonian Matrices -- The General Linear Normalization -- Stability of Equilibria -- Stability of Linear Hamiltonian Systems -- Parametric Resonance -- References -- Index. 330 $aThis book introduces the reader to the study of Hamiltonian systems, focusing on the stability of autonomous and periodic systems and expanding to topics that are usually not covered by the canonical literature in the field. It emerged from lectures and seminars given at the Federal University of Pernambuco, Brazil, known as one of the leading research centers in the theory of Hamiltonian dynamics. This book starts with a brief review of some results of linear algebra and advanced calculus, followed by the basic theory of Hamiltonian systems. The study of normal forms of Hamiltonian systems is covered by Ch.3, while Chapters 4 and 5 treat the normalization of Hamiltonian matrices. Stability in non-linear and linear systems are topics in Chapters 6 and 7. This work finishes with a study of parametric resonance in Ch. 8. All the background needed is presented, from the Hamiltonian formulation of the laws of motion to the application of the Krein-Gelfand-Lidskii theory of strongly stable systems. With a clear, self-contained exposition, this work is a valuable help to advanced undergraduate and graduate students, and to mathematicians and physicists doing research on this topic. 410 0$aApplied Mathematical Sciences,$x2196-968X ;$v218 606 $aDynamics 606 $aDifferential equations 606 $aMathematical physics 606 $aDynamical Systems 606 $aDifferential Equations 606 $aMathematical Physics 615 0$aDynamics. 615 0$aDifferential equations. 615 0$aMathematical physics. 615 14$aDynamical Systems. 615 24$aDifferential Equations. 615 24$aMathematical Physics. 676 $a514.74 676 $a512.944 700 $aCabral$b Hildeberto E.$01429659 702 $aBranda?o Dias$b Lu?cia 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910739408003321 996 $aNormal Forms and Stability of Hamiltonian Systems$93568839 997 $aUNINA