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Science/Engineering Embedding Problems In Symplectic Geometry

Posted on 2010-03-15




Name:Science/Engineering Embedding Problems In Symplectic Geometry
ASIN/ISBN:3110178761
Language:English
File size:1.61 Mb
ISBN: 3110178761
Publish Date: March 30, 2005
File Type: PDF (OCR)
Pages: 250 pages
File Size: 1.61 MB
Other Info: Walter de Gruyter
   Science/Engineering Embedding Problems In Symplectic Geometry

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Embedding Problems In Symplectic Geometry (De Gruyter Expositions in Mathematics): 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 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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