Introduction to Hamiltonian Dynamical Systems and the N-Body Problem

Softcover version of original hardcover Auflage 2009
ISBN: 978-1-4419-1886-4
Verlag: Springer

Buch, Englisch, Band 90, 399 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 635 g

Reihe: 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/.

Zielgruppe

Research

Autoren/Hrsg.

Meyer, Kenneth

Hall, Glen

Offin, Dan

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Physik Mechanik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

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.

Über Autor(innen)

Hall, Glen
Glen Hall is an associate professor at Boston University.

Meyer, Kenneth
Ken Meyer is an emeritus professor at the University of Cincinnati,

Offin, Dan
Dan Offin is a professor at Queen's University.

Ken Meyer is an emeritus professor at the University of Cincinnati, Glen Hall is an associate professor at Boston University, and Dan Offin is a professor at Queen's University.