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Embedding Problems in Symplectic Geometry (De Gruyter Expositions in Mathematics, 40) - Hardcover
Book 4 of 100: De Gruyter Expositions in Mathematics
Synopsis
Symplectic geometry is the geometry underlying Hamiltonian dynamics, and symplectic mappings arise as time-1-maps of Hamiltonian flows. The spectacular rigidity phenomena for symplectic mappings discovered in the last two decades show that certain things cannot be done by a symplectic mapping. For instance, Gromov's famous "non-squeezing'' theorem states that one cannot map a ball into a thinner cylinder by a symplectic embedding. The aim of this book is to show that certain other things can be done by symplectic mappings. This is achieved by various elementary and explicit symplectic embedding constructions, such as "folding", "wrapping'', and "lifting''. These constructions are carried out in detail and are used to solve some specific symplectic embedding problems.
The exposition is self-contained and addressed to students and researchers interested in geometry or dynamics.
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About the Author
Felix Schlenk is Postdoc at the Department of Mathematics of Leipzig University, Leipzig, Germany.
"About this title" may belong to another edition of this title.
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Embedding Problems in Symplectic Geometry
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Berlin, Walter de Gruyter, 2005
ISBN 10: 3110178761
ISBN 13: 9783110178760
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Embedding Problems in Symplectic Geometry (De Gruyter Expositions in Mathematics, 40)
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ISBN 10: 3110178761
ISBN 13: 9783110178760
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Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Symplectic geometry is the geometry underlying Hamiltonian dynamics, and symplectic mappings arise as time-1-maps of Hamiltonian flows. The spectacular rigidity phenomena for symplectic mappings discovered in the last two decades show that certain things cannot be done by a symplectic mapping. For instance, Gromov's famous 'non-squeezing'' theorem states that one cannot map a ball into a thinner cylinder by a symplectic embedding. The aim of this book is to show that certain other things can be done by symplectic mappings. This is achieved by various elementary and explicit symplectic embedding constructions, such as 'folding', 'wrapping'', and 'lifting''. These constructions are carried out in detail and are used to solve some specific symplectic embedding problems. The exposition is self-contained and addressed to students and researchers interested in geometry or dynamics. 260 pp. Englisch. Seller Inventory # 9783110178760
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