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.
From the reviews of the Russian edition:
"The main accent is shifted to the application. . .in geometrical
optics, thermostatics and control theory, and not to the
Hamiltonian mechanics only. . . . To make the book fairly
self-contained, full details of basic definitions and all proofs
are included. In this way, the majority of the text can be read
without the prerequisite of a course in geometry. The excellent
collection of examples illustrates the relatively hard and highly
abstract mathematical theory and its hidden difficulties.. . .The
book can rise real interest for specialists . . . . The . . . book
is a significant input in the modern symplectic geometry and its
applications."
(Andrey Tsiganov, St. Petersburg State University)"
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