Introduction to Hamiltonian Dynamical Systems and the N-Body Problem (Applied Mathematical Sciences)

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9781441918864: Introduction to Hamiltonian Dynamical Systems and the N-Body Problem (Applied Mathematical Sciences)

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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This text grew out of notes from a graduate course taught to students in mathematics and mechanical engineering. The goal was to take students who had some basic knowledge of differential equations and lead them through a systematic grounding in the theory of Hamiltonian systems, an introduction to the theory of integrals and reduction. Poincaré’s continuation of periodic solution, normal forms, and applications of KAM theory. There is a special chapter devoted to the theory of twist maps and various extensions of the classic Poincaré-Birkhoff fixed point theorem.

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Arising from a graduate course taught to math and engineering students, this text provides a systematic grounding in the theory of Hamiltonian systems, as well as introducing the theory of integrals and reduction. A number of other topics are covered too.

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Book Description Springer-Verlag New York Inc., United States, 2010. Paperback. Book Condition: New. 2nd ed. Softcover of orig. ed. 2009. 229 x 152 mm. Language: English . Brand New Book ***** Print on Demand *****.Thisneweditionexpandsonsomeoldmaterialandintroducessomene ws- 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.OurthanksgotoHildebe rto 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/. Bookseller Inventory # AAV9781441918864

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Book Description Springer-Verlag New York Inc., United States, 2010. Paperback. Book Condition: New. 2nd ed. Softcover of orig. ed. 2009. 229 x 152 mm. Language: English . Brand New Book ***** Print on Demand *****. 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.OurthanksgotoHildebe rto 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/. Bookseller Inventory # AAV9781441918864

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