Embedding Problems in Symplectic Geometry / / Felix Schlenk.
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 i...
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Superior document: | Title is part of eBook package: De Gruyter DG Expositions in Mathematics Backlist eBook Package |
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2008] ©2005 |
Year of Publication: | 2008 |
Language: | English |
Series: | De Gruyter Expositions in Mathematics ,
40 |
Online Access: | |
Physical Description: | 1 online resource (250 p.) :; Num. figs. |
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Other title: | Frontmatter -- Contents -- Introduction -- Proof of Theorem 1 -- Proof of Theorem 2 -- Multiple symplectic folding in four -- dimensions -- Symplectic folding in higher dimensions -- Proof of Theorem 3 -- Symplectic wrapping -- Proof of Theorem 4 -- Packing symplectic manifolds by hand -- Appendix -- Backmatter |
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Summary: | 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. |
Format: | Mode of access: Internet via World Wide Web. |
ISBN: | 9783110199697 9783110494969 9783110238570 9783110238471 9783110637205 9783110212129 9783110212136 9783110209082 |
ISSN: | 0938-6572 ; |
DOI: | 10.1515/9783110199697 |
Access: | restricted access |
Hierarchical level: | Monograph |
Statement of Responsibility: | Felix Schlenk. |