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The Resource Dynamical properties of diffeomorphisms of the annulus and of the torus, Patrice Le Calvez ; translated by Philippe Mazaud

Dynamical properties of diffeomorphisms of the annulus and of the torus, Patrice Le Calvez ; translated by Philippe Mazaud

Label
Dynamical properties of diffeomorphisms of the annulus and of the torus
Title
Dynamical properties of diffeomorphisms of the annulus and of the torus
Statement of responsibility
Patrice Le Calvez ; translated by Philippe Mazaud
Creator
Subject
Language
  • eng
  • fre
  • eng
Summary
  • "The first chapter of this monograph presents a survey of the theory of monotone twist maps of the annulus. First, the author covers the conservative case by presenting a short survey of Aubry-Mather theory and Birkhoff theory, followed by some criteria for existence of periodic orbits without the area-preservation property. These are applied in the area-decreasing case, and the properties of Birkhoff attractors are discussed. A diffeomorphism of the closed annulus which is isotopic to the identity can be written as the composition of monotone twist maps."
  • "The second chapter generalizes some aspects of Aubry-Mather theory to such maps and presents a version of the Poincare-Birkhoff theorem in which the periodic orbits have the same braid type as in the linear case. A diffeomorphism of the torus isotopic to the identity is also a composition of twist maps, and it is possible to obtain a proof of the Conley-Zehnder theorem with the same kind of conclusions about the braid type, in the case of periodic orbits. This results leads to an equivariant version of the Brouwer translation theorem which permits new proofs of some results about the rotation set of diffeomorphisms of the torus."--Jacket
Member of
Cataloging source
DLC
http://library.link/vocab/creatorName
Le Calvez, Patrice
Dewey number
514/.74
Illustrations
illustrations
Index
index present
LC call number
QA613.65
LC item number
.L4213 2000
Literary form
non fiction
Nature of contents
bibliography
Series statement
  • SMF/AMS texts and monographs
  • Astérisque
Series volume
  • v. 4
  • no. 204
http://library.link/vocab/subjectName
  • Diffeomorphisms
  • Differentiable dynamical systems
  • Mappings (Mathematics)
Label
Dynamical properties of diffeomorphisms of the annulus and of the torus, Patrice Le Calvez ; translated by Philippe Mazaud
Instantiates
Publication
Note
Originally published: France : Société Mathématique de France, c1991
Bibliography note
Includes bibliographical references (pages 101-105) and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 1.4.
  • Topological study of area-preserving twist maps: Birkhoff's theory.
  • 1.5.
  • The general case of twist diffeomorphisms.
  • 1.6.
  • A study of the dissipative case: Birkhoff attractors
  • Ch. 2.
  • Generating Phases of the Diffeomorphisms of the Torus and the Annulus.
  • 2.1.
  • Presentation of the results.
  • Ch. 1.
  • 2.2.
  • Composition of twist diffeomorphisms of the plane.
  • 2.3.
  • Existence of orbits with trivial braid type for conservative diffeomorphisms of the annulus
  • Presentation and Comparison of the Different Approaches to the Theory of Monotone Twist Diffeomorphisms of the Annulus.
  • 1.1.
  • Examples.
  • 1.2.
  • Definitions and notation: twist maps, rotation numbers.
  • 1.3.
  • Variational study of area-preserving twist diffeomorphisms: the Aubry-Mather theory.
Control code
43076813
Dimensions
26 cm
Extent
ix, 105 pages
Isbn
9780821819432
Lccn
99087060
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
Label
Dynamical properties of diffeomorphisms of the annulus and of the torus, Patrice Le Calvez ; translated by Philippe Mazaud
Publication
Note
Originally published: France : Société Mathématique de France, c1991
Bibliography note
Includes bibliographical references (pages 101-105) and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 1.4.
  • Topological study of area-preserving twist maps: Birkhoff's theory.
  • 1.5.
  • The general case of twist diffeomorphisms.
  • 1.6.
  • A study of the dissipative case: Birkhoff attractors
  • Ch. 2.
  • Generating Phases of the Diffeomorphisms of the Torus and the Annulus.
  • 2.1.
  • Presentation of the results.
  • Ch. 1.
  • 2.2.
  • Composition of twist diffeomorphisms of the plane.
  • 2.3.
  • Existence of orbits with trivial braid type for conservative diffeomorphisms of the annulus
  • Presentation and Comparison of the Different Approaches to the Theory of Monotone Twist Diffeomorphisms of the Annulus.
  • 1.1.
  • Examples.
  • 1.2.
  • Definitions and notation: twist maps, rotation numbers.
  • 1.3.
  • Variational study of area-preserving twist diffeomorphisms: the Aubry-Mather theory.
Control code
43076813
Dimensions
26 cm
Extent
ix, 105 pages
Isbn
9780821819432
Lccn
99087060
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations

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