Embedding problems in symplectic geometry / by Felix Schlenk.

Format:

Book

Author/Creator:

Schlenk, Felix, 1970-

Series:

Gruyter expositions in mathematics ; 40.

De Gruyter expositions in mathematics ; 40

Language:

English

Subjects (All):

Symplectic geometry.

Embeddings (Mathematics).

Physical Description:

1 online resource (260 p.)

Edition:

1st ed.

Place of Publication:

Berlin ; New York : Walter de Gruyter, c2005.

Language Note:

English

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.

Contents:

Front matter

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

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 241-246) and index.

ISBN:

9786612194818

9781282194816

128219481X

9783119159173

3119159174

9783110199697

3110199696

OCLC:

476023234