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
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The item Dynamical properties of diffeomorphisms of the annulus and of the torus, Patrice Le Calvez ; translated by Philippe Mazaud represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Dynamical properties of diffeomorphisms of the annulus and of the torus, Patrice Le Calvez ; translated by Philippe Mazaud represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 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 AubryMather theory and Birkhoff theory, followed by some criteria for existence of periodic orbits without the areapreservation property. These are applied in the areadecreasing 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 AubryMather theory to such maps and presents a version of the PoincareBirkhoff 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 ConleyZehnder 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
 Language

 eng
 fre
 eng
 Extent
 ix, 105 pages
 Note
 Originally published: France : Société Mathématique de France, c1991
 Contents

 1.4.
 Topological study of areapreserving 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 areapreserving twist diffeomorphisms: the AubryMather theory.
 Isbn
 9780821819432
 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
 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 AubryMather theory and Birkhoff theory, followed by some criteria for existence of periodic orbits without the areapreservation property. These are applied in the areadecreasing 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 AubryMather theory to such maps and presents a version of the PoincareBirkhoff 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 ConleyZehnder 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
 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
 Note
 Originally published: France : Société Mathématique de France, c1991
 Bibliography note
 Includes bibliographical references (pages 101105) 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 areapreserving 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 areapreserving twist diffeomorphisms: the AubryMather 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
 Note
 Originally published: France : Société Mathématique de France, c1991
 Bibliography note
 Includes bibliographical references (pages 101105) 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 areapreserving 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 areapreserving twist diffeomorphisms: the AubryMather 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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