Introduction to Symplectic and Hamiltonian Geometry
by Ana Cannas da Silva
Number of pages: 158
This text covers foundations of symplectic geometry in a modern language. We start by describing symplectic manifolds and their transformations, and by explaining connections to topology and other geometries. Next we study hamiltonian fields, hamiltonian actions and some of their practical applications in the context of mechanics and dynamical systems. We assume previous knowledge of the geometry of smooth manifolds, though the main required facts are collected in appendices.
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by Bjorn Ian Dundas - Johns Hopkins University
This is an elementary text book for the civil engineering students with no prior background in point-set topology. This is a rather terse mathematical text, but provided with an abundant supply of examples and exercises with hints.
by Uwe Kaiser - Boise State University
This is a preliminary version of introductory lecture notes for Differential Topology. We try to give a deeper account of basic ideas of differential topology than usual in introductory texts. Many examples of manifolds are worked out in detail.
by John Morgan, Gang Tian - American Mathematical Society
This book provides full details of a complete proof of the Poincare Conjecture following Grigory Perelman's preprints. The book is suitable for all mathematicians from advanced graduate students to specialists in geometry and topology.
by Ana Cannas da Silva - Princeton University
An overview of symplectic geometry – the geometry of symplectic manifolds. From a language of classical mechanics, symplectic geometry became a central branch of differential geometry and topology. This survey gives a partial flavor on this field.