Overview

Thisneweditionexpandsonsomeoldmaterialandintroducessomenews- jects. The expanded topics include: parametric stability, logarithms of s- plecticmatrices,normalformsforHamiltonianmatrices,spacialDelaunay- ements, pulsating coordinates, Lyapunov-Chetaev stability applications and more. There is a new section on the Maslov index and a new chapter on variational arguments as applied to the celebrated ?gure-eight orbit of the 3-body problem. Still the beginning chapters can serve as a ?rst graduate level course on Hamiltonian dynamical systems, but there is far too much material for a s- gle course. Instructors will have to select chapters to meet their interests and the needs of their class. It will also serve as a reference text and introduction to the literature. The authors wish to thank their wives and families for giving them the time to work on this project. They acknowledge the support of their univer- ties and various funding agencies including the National Science Foundation, the Taft Foundation, the Sloan Foundation, and the Natural Sciences and Engineering Research Council through the Discovery Grants Program. Thissecondeditioninmanuscriptformwasreadbymanyindividualswho mademanyvaluablesuggestionsandcorrections.OurthanksgotoHildeberto Cabral, Scott Dumas, Vadin Fitton, Clarissa Howison, Jesus ' Palaci' an, Dieter Schmidt, Jaume Soler, Qiudong Wang, and Patricia Yanguas. Nonetheless, it is the readers responsibility to inform us of additional er- ? rors.LookforemailaddressesandanerrataonMATH.UC.EDU/ MEYER/.

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From the 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) This is an interesting book on Hamiltonian systems, which is conceived as a first course at the graduate level. ... the book has two parts. The first one includes seven chapters and is more introductory in nature. ... The second part contains the most interesting and advanced material of the book. ... The book ... constitutes a very complete course on the theory of Hamiltonian systems. (Narciso Roman-Roy, Zentralblatt MATH, Vol. 1179, 2010)

From the 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)

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