Download Hamiltonian structures and generating families by Sergio Benenti PDF

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.

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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 . . . . ........... ... ... . . . . . . . . . .. ... ... . . . .. . . . . . . .... ... ... ... . . . . .

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