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- catalog abstract "The group of symplectic diffeomorphisms of a symplectic manifold plays a fundamental role both in geometry and classical mechanics. What is the minimal amount of energy required in order to generate a given mechanical motion? This variational problem admits an interpretation in terms of a remarkable geometry on the group discovered by Hofer in 1990. Hofer's geometry serves as a source of interesting problems and gives rise to new methods and notions which extend significantly our vision of the symplectic world. In the past decade this new geometry has been intensively studied in the framework of symplectic topology with the use of modern techniques such as Gromov's theory of pseudo-holomorphic curves, Floer homology and Guillemin-Sternberg-Lerman theory of symplectic connections. Furthermore, it opens up the intriguing prospect of using an alternative geometric intuition in dynamics. The book provides an essentially self-contained introduction into these developments and includes recent results on diameter, geodesics and growth of one-parameter subgroups in Hofer's geometry, as well as applications to dynamics and ergodic theory. It is addressed to researchers and students from the graduate level onwards.".
- catalog alternative "Geometry of the group of symplectic diffeomorphisms".
- catalog contributor b12145579.
- catalog created "c2001.".
- catalog date "2001".
- catalog date "c2001.".
- catalog dateCopyrighted "c2001.".
- catalog description "Includes bibliographical references (p. [125]-129) and index.".
- catalog description "The group of symplectic diffeomorphisms of a symplectic manifold plays a fundamental role both in geometry and classical mechanics. What is the minimal amount of energy required in order to generate a given mechanical motion? This variational problem admits an interpretation in terms of a remarkable geometry on the group discovered by Hofer in 1990. Hofer's geometry serves as a source of interesting problems and gives rise to new methods and notions which extend significantly our vision of the symplectic world. In the past decade this new geometry has been intensively studied in the framework of symplectic topology with the use of modern techniques such as Gromov's theory of pseudo-holomorphic curves, Floer homology and Guillemin-Sternberg-Lerman theory of symplectic connections. Furthermore, it opens up the intriguing prospect of using an alternative geometric intuition in dynamics. The book provides an essentially self-contained introduction into these developments and includes recent results on diameter, geodesics and growth of one-parameter subgroups in Hofer's geometry, as well as applications to dynamics and ergodic theory. It is addressed to researchers and students from the graduate level onwards.".
- catalog extent "xii, 132 p. :".
- catalog identifier "0817664327 (alk. paper)".
- catalog identifier "3764364327 (alk. paper)".
- catalog isPartOf "Lectures in mathematics ETH Zürich".
- catalog issued "2001".
- catalog issued "c2001.".
- catalog language "eng".
- catalog publisher "Basel ; Boston : Birkhauser Verlag,".
- catalog subject "516.3/62 21".
- catalog subject "Diffeomorphisms.".
- catalog subject "Hamiltonian systems.".
- catalog subject "Mathematics.".
- catalog subject "QA649 .P64 2001".
- catalog subject "Symplectic manifolds.".
- catalog title "Geometry of the group of symplectic diffeomorphisms".
- catalog title "The geometry of the group of symplectic diffeomorphism / Leonid Polterovich.".
- catalog type "text".