ENGLISH

Embedding Problems in Symplectic Geometry

By Felix Schlenk

Book information

Publisher
de Gruyter
Year
2005
ISBN
9783110199697, 9783110178760
DOI
10.1515/9783110199697
Language
english
Format
PDF
Filesize
1 MB (1436056 bytes)
Series
De Gruyter Expositions in Mathematics; 40
Pages
260\260
Library
degruyter.com
Time added
2023-07-29 08:19:06

Description

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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