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Notes on Hamiltonian Dynamical Systems

2022-05-05 Science
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Release : 2022-05-05
Genre : Science
Kind : eBook
Book Rating : 142/5 ( reviews)

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Book Synopsis Notes on Hamiltonian Dynamical Systems by : Antonio Giorgilli

Download or read book Notes on Hamiltonian Dynamical Systems written by Antonio Giorgilli. This book was released on 2022-05-05. Available in PDF, EPUB and Kindle. Book excerpt: Introduces Hamiltonian dynamics from the very beginning, culminating in the most important recent results: Kolmogorov's and Nekhoroshev's.

Notes on Dynamical Systems

2005 Mathematics
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Release : 2005
Genre : Mathematics
Kind : eBook
Book Rating : 777/5 ( reviews)

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Book Synopsis Notes on Dynamical Systems by : Jürgen Moser

Download or read book Notes on Dynamical Systems written by Jürgen Moser. This book was released on 2005. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the field of dynamical systems, in particular, to the special class of Hamiltonian systems. The authors aimed at keeping the requirements of mathematical techniques minimal but giving detailed proofs and many examples and illustrations from physics and celestial mechanics. After all, the celestial $N$-body problem is the origin of dynamical systems and gave rise in the past to many mathematical developments. Jurgen Moser (1928-1999) was a professor atthe Courant Institute, New York, and then at ETH Zurich. He served as president of the International Mathematical Union and received many honors and prizes, among them the Wolf Prize in mathematics. Jurgen Moser is the author of several books, among them Stable and Random Motions in DynamicalSystems. Eduard Zehnder is a professor at ETH Zurich. He is coauthor with Helmut Hofer of the book Symplectic Invariants and Hamiltonian Dynamics. Information for our distributors: Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.

Hamiltonian Dynamical Systems and Applications

2008-02-17 Mathematics
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Release : 2008-02-17
Genre : Mathematics
Kind : eBook
Book Rating : 642/5 ( reviews)

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Book Synopsis Hamiltonian Dynamical Systems and Applications by : Walter Craig

Download or read book Hamiltonian Dynamical Systems and Applications written by Walter Craig. This book was released on 2008-02-17. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems. Applications are also presented to several important areas of research, including problems in classical mechanics, continuum mechanics, and partial differential equations.

Introduction to Hamiltonian Dynamical Systems and the N-Body Problem

2017-05-04 Mathematics
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Release : 2017-05-04
Genre : Mathematics
Kind : eBook
Book Rating : 915/5 ( reviews)

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Book Synopsis Introduction to Hamiltonian Dynamical Systems and the N-Body Problem by : Kenneth R. Meyer

Download or read book Introduction to Hamiltonian Dynamical Systems and the N-Body Problem written by Kenneth R. Meyer. This book was released on 2017-05-04. Available in PDF, EPUB and Kindle. Book excerpt: This third edition text provides expanded material on the restricted three body problem and celestial mechanics. With each chapter containing new content, readers are provided with new material on reduction, orbifolds, and the regularization of the Kepler problem, all of which are provided with applications. The previous editions grew out of graduate level courses in mathematics, engineering, and physics given at several different universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. This text provides a mathematical structure of celestial mechanics ideal for beginners, and will be useful to graduate students and researchers alike. Reviews of the second edition: "The primary subject here is the basic theory of Hamiltonian differential equations studied from the perspective of differential dynamical systems. The N-body problem is used as the primary example of a Hamiltonian system, a touchstone for the theory as the authors develop it. This book is intended to support a first course at the graduate level for mathematics and engineering students. ... It is a well-organized and accessible introduction to the subject ... . This is an attractive book ... ." (William J. Satzer, The Mathematical Association of America, March, 2009) “The second edition of this text infuses new mathematical substance and relevance into an already modern classic ... and is sure to excite future generations of readers. ... This outstanding book can be used not only as an introductory course at the graduate level in mathematics, but also as course material for engineering graduate students. ... it is an elegant and invaluable reference for mathematicians and scientists with an interest in classical and celestial mechanics, astrodynamics, physics, biology, and related fields.” (Marian Gidea, Mathematical Reviews, Issue 2010 d)

Notes on Hamiltonian Dynamical Systems Notes on Hamiltonian Dynamical Systems

2022-05-05 Science
Download Notes on Hamiltonian Dynamical Systems Notes on Hamiltonian Dynamical Systems PDF Online Free

Author :
Release : 2022-05-05
Genre : Science
Kind : eBook
Book Rating : 86X/5 ( reviews)

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Book Synopsis Notes on Hamiltonian Dynamical Systems Notes on Hamiltonian Dynamical Systems by : Antonio Giorgilli

Download or read book Notes on Hamiltonian Dynamical Systems Notes on Hamiltonian Dynamical Systems written by Antonio Giorgilli. This book was released on 2022-05-05. Available in PDF, EPUB and Kindle. Book excerpt: 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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