Kenneth Meyer, Glen Hall, Dan Offin

Introduction to Hamiltonian Dynamical Systems and the N-Body Problem (eBook, PDF)

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Springer US
• Seitenzahl: 399
• Erscheinungstermin: 5. Dezember 2008
• Englisch
• ISBN-13: 9780387097244
• Artikelnr.: 37286538

Autorenporträt

Ken Meyer  has a long history of working in Hamiltonian differential equations and the N-body problem.  He has over 100 papers published.     Daniel Offin is an active researcher in the theory of Hamiltonian systems using variational methods. He has made some important contributions to celestial mechanics using the Maslov index.

Inhaltsangabe

Beginnings.- Hamiltonian Systems.- Celestial Mechanics.- The Restricted Problem.- Topics in Linear Theory.- Local Geometric Theory.- Symplectic Geometry.- Special Coordinates.- Poincaré's Continuation Method.- Normal Forms.- Bifurcations of Periodic Orbits.- Stability and KAM Theory.- Variational Techniques.

Rezensionen

"The book begins as an elementary introduction to the theory of Hamiltonian systems, taking as a starting point Hamiltonian systems of differential equations and explaining the interesting features they have with the help of classical examples. ... the book can be used at an advanced undergraduate or beginning graduate level as an introduction to these subjects, in particular when one is interested in their impact on classical (celestial) mechanics." (Johannes Giannoulis, zbMATH 1372.70002, 2017)