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In recent years scholars from a variety of branches of mathematics have made several significant developments in the theory of group actions. Groups of Circle D
The Geometry of Infinite-Dimensional Groups
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This monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrab
The Structure of Classical Diffeomorphism Groups
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In the 60's, the work of Anderson, Chernavski, Kirby and Edwards showed that the group of homeomorphisms of a smooth manifold which are isotopic to the identity
Structure and Regularity of Group Actions on One-Manifolds
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This book presents the theory of optimal and critical regularities of groups of diffeomorphisms, from the classical work of Denjoy and Herman, up through recent
The Geometry of the Group of Symplectic Diffeomorphism
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Authors: Leonid Polterovich
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The group of Hamiltonian diffeomorphisms Ham(M, 0) of a symplectic mani fold (M, 0) plays a fundamental role both in geometry and classical mechanics. For a geo