Symplectic Invariants and Hamiltonian Dyna...

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Beschreibung

The discoveries of the last decades have opened new perspectives for the old field of Hamiltonian systems and led to the creation of a new field: symplectic topology. Surprising rigidity phenomena demonstrate that the nature of symplectic mappings is very different from that of volume preserving mappings. This raises new questions, many of them still unanswered. On the other hand, analysis of an old variational principle in classical mechanics has established global periodic phenomena in Hamiltonian systems. As it turns out, these seemingly different phenomena are mysteriously related. One of the links is a class of symplectic invariants, called symplectic capacities. These invariants are the main theme of this book, which includes such topics as basic symplectic geometry, symplectic capacities and rigidity, periodic orbits for Hamiltonian systems and the action principle, a bi-invariant metric on the symplectic diffeomorphism group and its geometry, symplectic fixed point theory, the Arnold conjectures and first order elliptic systems, and finally a survey on Floer homology and symplectic homology.
The exposition is self-contained and addressed to researchers and students from the graduate level onwards.

Über den Autor

Helmut Hofer is Professor at the Institute for Advanced Study in Princeton, New Jersey, USA.

Eduard Zehnder is emeritus Professor of ETH Zürich, Switzerland.

Zusammenfassung

Opened new perspectives for the old field of Hamiltonian systems and let to the creation of a new field: symplectic topology

Invariants which grew out of lectures given by the authors

Selection by a single principle: the action principle of mechanics

Includes supplementary material: [...]

Inhaltsverzeichnis

1 Introduction.- 2 Symplectic capacities.- 3 Existence of a capacity.- 4 Existence of closed characteristics.- 5 Compactly supported symplectic mappings in R2n.- 6 The Arnold conjecture, Floer homology and symplectic homology.- Appendix.- Index.- Bibliography.

Details

Erscheinungsjahr:	2011
Fachbereich:	Geometrie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	356
Reihe:	Modern Birkhäuser Classics
Inhalt:	xiv 341 S. 49 s/w Illustr. 341 p. 49 illus.
ISBN-13:	9783034801034
ISBN-10:	3034801033
Sprache:	Englisch
Herstellernummer:	80030372
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Zehnder, Eduard Hofer, Helmut
Auflage:	Reprint of the First Edition 1994.
Hersteller:	Springer Basel Springer Basel AG Modern Birkhäuser Classics
Maße:	235 x 155 x 20 mm
Von/Mit:	Eduard Zehnder (u. a.)
Erscheinungsdatum:	02.04.2011
Gewicht:	0,54 kg

preigu-id: 107038128