Shortcuts
Top of page (Alt+0)
Page content (Alt+9)
Page menu (Alt+8)
Your browser does not support javascript, some WebOpac functionallity will not be available.
.
Default
.
PageMenu
-
Main Menu
-
Simple Search
.
Advanced Search
.
Journal Search
.
Refine Search Results
.
Preferences
.
Search Menu
Simple Search
.
Advanced Search
.
New Items Search
.
Journal Search
.
Refine Search Results
.
Bottom Menu
Help
Italian
.
English
.
German
.
New Item Menu
New Items Search
.
New Items List
.
Links
SISSA Library
.
ICTP library
.
Italian National web catalog (SBN)
.
Trieste University web catalog
.
Udine University web catalog
.
© LIBERO v6.4.1sp220816
Page content
You are here
:
Catalogue Display
Catalogue Display
Symplectic Invariants and Hamiltonian Dynamics
.
Bookmark this Record
Catalogue Record 47341
.
.
Author info on Wikipedia
.
.
LibraryThing
.
.
Google Books
.
.
Amazon Books
.
Catalogue Information
Catalogue Record 47341
.
Reviews
Catalogue Record 47341
.
British Library
Resolver for RSN-47341
Google Scholar
Resolver for RSN-47341
WorldCat
Resolver for RSN-47341
Catalogo Nazionale SBN
Resolver for RSN-47341
GoogleBooks
Resolver for RSN-47341
ICTP Library
Resolver for RSN-47341
.
Share Link
Jump to link
Catalogue Information
Field name
Details
Dewey Class
516.36
Title
Symplectic Invariants and Hamiltonian Dynamics ([EBook]) / by Helmut Hofer, Eduard Zehnder
Author
Hofer, Helmut. , 1956-
Added Personal Name
Zehnder, Eduard
Other name(s)
SpringerLink (Online service)
Publication
Basel : Birkhäuser , 1994
Physical Details
XIII, 346 p. 2 illus. : online resource.
Series
Birkhäuser Advanced Texts / Basler Lehrbücher
ISBN
9783034885409
Summary Note
The discoveries of the past decade 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 map pings is very different from that of volume preserving mappings which raised new questions, many of them still unanswered. On the other hand, due to the analysis of an old variational principle in classical mechanics, global periodic phenomena in Hamiltonian systems have been established. As it turns out, these seemingly differ ent 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 grew out of lectures given by the authors at Rutgers University, the RUB Bochum and at the ETH Zurich (1991) and also at the Borel Seminar in Bern 1992. Since the lectures did not require any previous knowledge, only a few and rather elementary topics were selected and proved in detail. Moreover, our se lection has been prompted by a single principle: the action principle of mechanics. The action functional for loops in the phase space, given by 1 Fh) = J pdq -J H(t, 'Y(t)) dt , 'Y 0 differs from the old Hamiltonian principle in the configuration space defined by a Lagrangian. The critical points of F are those loops 'Y which solve the Hamiltonian equations associated with the Hamiltonian H and hence are the periodic orbits.:
Contents note
1 Introduction -- 1.1 Symplectic vector spaces -- 1.2 Symplectic diffeomorphisms and Hamiltonian vector fields -- 1.3 Hamiltonian vector fields and symplectic manifolds -- 1.4 Periodic orbits on energy surfaces -- 1.5 Existence of a periodic orbit on a convex energy surface -- 1.6 The problem of symplectic embeddings -- 1.7 Symplectic classification of positive definite quadratic forms -- 1.8 The orbit structure near an equilibrium, Birkhoff normal form -- 2 Symplectic capacities -- 2.1 Definition and application to embeddings -- 2.2 Rigidity of symplectic diffeomorphisms -- 3 Existence of a capacity -- 3.1 Definition of the capacity c0 -- 3.2 The minimax idea -- 3.3 The analytical setting -- 3.4 The existence of a critical point -- 3.5 Examples and illustrations -- 4 Existence of closed characteristics -- 4.1 Periodic solutions on energy surfaces -- 4.2 The characteristic line bundle of a hypersurface -- 4.3 Hypersurfaces of contact type, the Weinstein conjecture -- 4.4 “Classical” Hamiltonian systems -- 4.5 The torus and Herman’s Non-Closing Lemma -- 5 Compactly supported symplectic mappings in ?2n -- 5.1 A special metric d for a group D of Hamiltonian diffeomorphisms -- 5.2 The action spectrum of a Hamiltonian map -- 5.3 A “universal” variational principle -- 5.4 A continuous section of the action spectrum bundle -- 5.5 An inequality between the displacement energy and the capacity -- 5.6 Comparison of the metric d on D with the C0-metric -- 5.7 Fixed points and geodesics on D -- 6 The Arnold conjecture, Floer homology and symplectic homology -- 6.1 The Arnold conjecture on symplectic fixed points -- 6.2 The model case of the torus -- 6.3 Gradient-like flows on compact spaces -- 6.4 Elliptic methods and symplectic fixed points -- 6.5 Floer’s appraoch to Morse theory for the action functional -- 6.6 Symplectic homology -- A.2 Action-angle coordinates, the Theorem of Arnold and Jost -- A.4 The Cauchy-Riemann operator on the sphere -- A.5 Elliptic estimates near the boundary and an application -- A.6 The generalized similarity principle -- A.7 The Brouwer degree -- A.8 Continuity property of the Alexander-Spanier cohomology.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-3-0348-8540-9
Links to Related Works
Subject References:
Analysis
.
Analysis (Mathematics)
.
Complex manifolds
.
Differential Geometry
.
Manifolds and Cell Complexes (incl. Diff.Topology)
.
Manifolds (Mathematics)
.
Mathematical analysis
.
Mathematics
.
Authors:
author
.
Hofer, Helmut. 1956-
.
Zehnder, Eduard
.
Corporate Authors:
SpringerLink (Online service)
.
Series:
Birkhäuser Advanced Texts / Basler Lehrbücher
.
Classification:
516.36
.
.
ISBD Display
Catalogue Record 47341
.
Tag Display
Catalogue Record 47341
.
Related Works
Catalogue Record 47341
.
Marc XML
Catalogue Record 47341
.
Add Title to Basket
Catalogue Record 47341
.
Catalogue Information 47341
Beginning of record
.
Catalogue Information 47341
Top of page
.
Download Title
Catalogue Record 47341
Export
This Record
As
Labelled Format
Bibliographic Format
ISBD Format
MARC Format
MARC Binary Format
MARCXML Format
User-Defined Format:
Title
Author
Series
Publication Details
Subject
To
File
Email
Reviews
This item has not been rated.
Add a Review and/or Rating
47341
1
47341
-
2
47341
-
3
47341
-
4
47341
-
5
47341
-
Quick Search
Search for