Introduction to Hamiltonian Dynamical Systems and the N-body Problem
Seiten
2010
|
2nd ed. Softcover of orig. ed. 2009
Springer-Verlag New York Inc.
978-1-4419-1886-4 (ISBN)
Springer-Verlag New York Inc.
978-1-4419-1886-4 (ISBN)
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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.
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/.
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/.
Hamiltonian Systems.- Equations of Celestial Mechanics.- Linear Hamiltonian Systems.- Topics in Linear Theory.- Exterior Algebra and Differential Forms.- Symplectic Transformations.- Special Coordinates.- Geometric Theory.- Continuation of Solutions.- Normal Forms.- Bifurcations of Periodic Orbits.- Variational Techniques.- Stability and KAM Theory.- Twist Maps and Invariant Circle.
| Erscheint lt. Verlag | 29.11.2010 |
|---|---|
| Reihe/Serie | Applied Mathematical Sciences ; 90 | Applied Mathematical Sciences ; 90 |
| Zusatzinfo | biography |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 581 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Naturwissenschaften ► Physik / Astronomie | |
| ISBN-10 | 1-4419-1886-8 / 1441918868 |
| ISBN-13 | 978-1-4419-1886-4 / 9781441918864 |
| Zustand | Neuware |
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