Embedding Problems in Symplectic Geometry

1. Auflage 2005
ISBN: 978-3-11-017876-0
Verlag: De Gruyter

Buch, Englisch, Band 40, 250 Seiten, HC runder Rücken kaschiert, Format (B × H): 175 mm x 246 mm, Gewicht: 625 g

Reihe: De Gruyter Expositions in Mathematics

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.

Zielgruppe

Research Mathematicians, Students, Academic Libraries

Autoren/Hrsg.

Schlenk, Felix

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Elementare Geometrie: Allgemeines
• Mathematik | Informatik Mathematik Topologie Analytische Topologie
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Über Autor(innen)

Felix Schlenk is Postdoc at the Department of Mathematics of Leipzig University, Leipzig, Germany.