Symplectic Geometry of Integrable Hamiltonian Systems
Produktdetaljer
"This book, an expanded version of the lectures delivered by the authors at the 'Centre de Recerca Matematica' Barcelona in July 2001, is designed for a modern introduction to symplectic and contact geometry to graduate students. It can also be useful to research mathematicians interested in integrable systems. The text includes up-to-date references, and has three parts. The first part, by Michele Audin, contains an introduction to Lagrangian and special Lagrangian submanifolds in symplectic and Calabi-Yau manifolds... The second part, by Ana Cannas da Silva, provides an elementary introduction to toric manifolds (i.e. smooth toric varieties)... In these first two parts, there are exercises designed to complement the exposition or extend the reader's understanding... The last part, by Eugene Lerman, is devoted to the topological study of these manifolds." -ZENTRALBLATT MATH
Among all the Hamiltonian systems, the integrable ones have special geometric properties; The quasi-periodicity of the solutions of an integrable system is a result of the fact that the system is invariant under a (semi-global) torus action.