By Sergio Benenti

This ebook is an more desirable model of an prior Russian variation. in addition to thorough revisions, extra emphasis was once wear reordering the subjects in accordance with a category-theoretical view. this permits the mathematical effects to be said, proved, and understood in a miles more uncomplicated and chic way.

From the stories of the Russian edition:

"The major accessory is shifted to the appliance . . . in geometrical optics, thermostatics and regulate idea, and never to the Hamiltonian mechanics purely. . . . To make the e-book really self-contained, complete information of uncomplicated definitions and all proofs are integrated. during this manner, the vast majority of the textual content will be learn with no the prerequisite of a direction in geometry. the wonderful choice of examples illustrates the quite challenging and hugely summary mathematical conception and its hidden problems. . . . The publication can upward thrust actual curiosity for experts . . . . The . . . e-book is an important enter within the glossy symplectic geometry and its applications."

(Andrey Tsiganov, St. Petersburg kingdom University)

Sergio Benenti is a professor of mathematical physics at Universit� di Torino, Italy. His present fields of study contain symplectic geometry with purposes to actual theories, Riemannian geometry with functions to the speculation of the separation of variables within the Hamilton-Jacobi equation and in different proper differential equations of physics, and mathematical types of the dynamics of non-holonomic systems.

**Read Online or Download Hamiltonian structures and generating families PDF**

**Similar differential geometry books**

The Surveys in Differential Geometry are supplementations to the magazine of Differential Geometry, that are released by means of foreign Press. They contain major invited papers combining unique learn and overviews of the most up-tp-date examine in particular parts of curiosity to the growing to be magazine of Differential Geometry group.

**Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics**

Critical transforms, resembling the Laplace and Fourier transforms, were significant instruments in arithmetic for a minimum of centuries. within the final 3 a long time the advance of a few novel principles in algebraic geometry, classification idea, gauge conception, and string idea has been heavily on the topic of generalizations of fundamental transforms of a extra geometric personality.

**Riemannsche Geometrie im Großen**

Aus dem Vorwort: "Globale Probleme der Differentialgeometrie erfreuen sich eines immer noch wachsenden Interesses. Gerade in der Riemannschen Geometrie hat die Frage nach Beziehungen zwischen Riemannscher und topologischer Struktur in neuerer Zeit zu vielen sch? nen und ? berraschenden Einsichten gef?

**Geometric analysis and function spaces**

This booklet brings into concentration the synergistic interplay among research and geometry through studying numerous subject matters in functionality concept, genuine research, harmonic research, numerous complicated variables, and crew activities. Krantz's method is encouraged by way of examples, either classical and glossy, which spotlight the symbiotic dating among research and geometry.

- An Introduction to Differential Manifolds
- Dynamical Systems IV: Symplectic Geometry and its Applications
- Geometric Nonlinear Functional Analysis: 1
- Theory of moduli: lectures given at the 3rd 1985 session of the Centro internazionale matematico estivo

**Extra info for Hamiltonian structures and generating families**

**Sample text**

Because of the definition of submersion, this linear relation is the graph of a surjective linear map. Thus, T(p0 ,p) R is a linear symplectic reduction, with inverse image Tp C. (T(p0 ,p) R) ◦ Tp0 M0 = Tp C. 3, items (i) and (iii) are proved (note that M0 is coisotropic). Moreover, (T(p0 ,p) R) ◦ {0} = Tp§ C, 0 ∈ Tp0 M0 . Let us consider the fiber Ip0 = R ◦ {p0 }. We have Tp Ip0 = {v ∈ Tp C such that T ρ(v) = 0} = {v ∈ Tp C such that T(p,p0 ) R ◦ {v} = 0} = (T(p0 ,p) R) ◦ {0} = Tp§ C. 46 3 Symplectic Relations on Symplectic Manifolds This shows that the tangent space of a fiber at a point p coincides with the tangent space of the characteristic containing that point.

T K⊆T K T K ··· ····· · · · · ···· ···•· p T K ····· · · · ·· ···· K coisotropic (M, ω) Fig. 2 Coisotropic submanifold ... ... ... ... ............ ............. .......... ... ........ . . . . ..... § ... . .................................. . . . ..... ... ..... . . p . p . . . . ........... ... ... . . . . . . . . . .. ... ... . . . .. . . . . . . .... ... ... ... . . . . .