Hamiltonian Structures and Generating Families

This book is an enhanced version of an earlier Russian edition. Besides thorough revisions, more emphasis was put on reordering the topics according to a category-theoretical view. This allows the mathematical results to be stated, proved, and understood in a much easier and elegant way. "The . . . book is a significant input in the modern symplectic geometry and its applications." (Andrey Tsiganov, St. Petersburg State University)

Enhanced version of Russian first edition Focuses on Hamiltonian mechanics, as well as the application of modern mathematical methods of symplectic geometry and topology in geometrical optics, thermostatics and control theory Self-contained with full details of basic notions of calculus on manifolds in the first two chapters Includes supplementary material: sn.pub/extras

Auteur
Sergio Benenti is a professor of mathematical physics at Università di Torino, Italy. His current fields of research include symplectic geometry with applications to physical theories, Riemannian geometry with applications to the theory of the separation of variables in the Hamilton-Jacobi equation and in other relevant differential equations of physics, and mathematical models of the dynamics of non-holonomic systems.

Contenu

Preface.- Basic Notions of Calculus on Manifolds.- Relations.- Symplectic Relations on Symplectic Manifolds.- Symplectic Relations on Cotangent Bundles.- Canonical Lift on Cotangent Bundles.-The Geometry of the Hamilton-Jacobi Equation.- Hamiltonian Optics in Euclidean Spaces.- Control of Static Systems.- Supplementary Topics.- Global Hamilton Principal Functions on S2 and H2.- References.- Index.