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Notes on Hamiltonian dynamical systems /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Notes on Hamiltonian dynamical systems // Antonio Giorgilli, University of Milan.
作者:	Giorgilli, Antonio,
面頁冊數:	1 online resource (xix, 451 pages) :digital, PDF file(s). :
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 (ebook)

Notes on Hamiltonian dynamical systems /
Giorgilli, Antonio,

Notes on Hamiltonian dynamical systems /Antonio Giorgilli, University of Milan. - 1 online resource (xix, 451 pages) :digital, PDF file(s). - 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 (ebook)Subjects--Topical Terms:

672650
Hamiltonian systems.

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

Dewey Class. No.: 515/.39

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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.
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