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Notes on Hamiltonian dynamical systems

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Notes on Hamiltonian dynamical systemsAntonio Giorgilli, University of Milan.
作者:	Giorgilli, Antonio.
出版者:	Cambridge :Cambridge University Press,2022.
面頁冊數:	xix, 451 p. :ill., digital ;23 cm.
附註:	Title from publisher's bibliographic system (viewed on 07 Apr 2022).
標題:	Hamiltonian systems.
電子資源:	https://doi.org/10.1017/9781009151122
ISBN:	9781009151122$q(electronic bk.)

Notes on Hamiltonian dynamical systems
Giorgilli, Antonio.

Notes on Hamiltonian dynamical systems[electronic resource] /Antonio Giorgilli, University of Milan. - Cambridge :Cambridge University Press,2022. - xix, 451 p. :ill., digital ;23 cm. - London Mathematical Society student texts ;102. - London Mathematical Society student texts ;81..

Title from publisher's bibliographic system (viewed on 07 Apr 2022).

Starting with the basics of Hamiltonian dynamics and canonical transformations, this text follows the historical development of the theory culminating in recent results: the Kolmogorov-Arnold-Moser theorem, Nekhoroshev's theorem and superexponential stability. Its analytic approach allows students to learn about perturbation methods leading to advanced results. Key topics covered include Liouville's theorem, the proof of Poincaré's non-integrability theorem and the nonlinear dynamics in the neighbourhood of equilibria. The theorem of Kolmogorov on persistence of invariant tori and the theory of exponential stability of Nekhoroshev are proved via constructive algorithms based on the Lie series method. A final chapter is devoted to the discovery of chaos by Poincaré and its relations with integrability, also including recent results on superexponential stability. Written in an accessible, self-contained way with few prerequisites, this book can serve as an introductory text for senior undergraduate and graduate students.

ISBN: 9781009151122$q(electronic bk.)Subjects--Topical Terms:

207807
Hamiltonian systems.

LC Class. No.: QA614.83 / .G56 2022

Dewey Class. No.: 515.39

Notes on Hamiltonian dynamical systems
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490 1 $a London Mathematical Society student texts ; $v 102
500 $a Title from publisher's bibliographic system (viewed on 07 Apr 2022).
520 $a Starting with the basics of Hamiltonian dynamics and canonical transformations, this text follows the historical development of the theory culminating in recent results: the Kolmogorov-Arnold-Moser theorem, Nekhoroshev's theorem and superexponential stability. Its analytic approach allows students to learn about perturbation methods leading to advanced results. Key topics covered include Liouville's theorem, the proof of Poincaré's non-integrability theorem and the nonlinear dynamics in the neighbourhood of equilibria. The theorem of Kolmogorov on persistence of invariant tori and the theory of exponential stability of Nekhoroshev are proved via constructive algorithms based on the Lie series method. A final chapter is devoted to the discovery of chaos by Poincaré and its relations with integrability, also including recent results on superexponential stability. Written in an accessible, self-contained way with few prerequisites, this book can serve as an introductory text for senior undergraduate and graduate students.
650 0 $a Hamiltonian systems. $3 207807
830 0 $a London Mathematical Society student texts ; $v 81. $3 810761
856 4 0 $u https://doi.org/10.1017/9781009151122