000			nam a22 4500
999			_c33093 _d33093
008			240320b xxu||||| |||| 00| 0 eng d
020			_a9783031330452
082			_a512.944 _bCAB
100			_aCabral, Hildeberto
245			_aNormal forms and stability of Hamiltonian systems
260			_bSpringer, _c2023 _aCham :
300			_axxi, 337 p. ; _bill., _c24 cm
365			_b74.99 _c€ _d93.50
490			_aApplied mathematical sciences
504			_aIncludes bibliographical references and index.
520			_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.
650			_aHamiltonian systems
650			_aDynamical systems
650			_aBirkhoff normal form
650			_aArnold theorem
650			_aKrein-Gelfand-Lidskii theorem
650			_aDeprit-Hori method
650			_aHomogeneous polynomia
650			_aLagrangian subspace
700			_aBrandao Dias, Lucia
942			_2ddc _cBK