Lie Group Actions
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One of the main themes of this book is the notion of symmetry. The main goal in the chapters at the core of this book is explaining to the reader how the symmetries of a Hamiltonian dynamical system can be used to simplify or reduce the study of that system. From the mathematical point of view the description of symmetries is implemented via the use of Lie group actions and, more generally, pseudogroups and groupoids. In the following two chapters we review all the material concerning these topics that will be needed in the rest of the book.