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
Illustrations
illustrations
Index
index present
LC call number
QA613.65
LC item number
.L4213 2000
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/subjectName
  • Diffeomorphisms
  • Differentiable dynamical systems
  • Mappings (Mathematics)
  • Diffeomorphisms
  • Differentiable dynamical systems
  • Mappings (Mathematics)
  • Torus
  • Diffeomorphismus
  • Kreisring
Label
Dynamical properties of diffeomorphisms of the annulus and of the torus, Patrice Le Calvez ; translated by Philippe Mazaud
Instantiates
Publication
Bibliography note
Includes bibliographical references (p 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.
Dimensions
25 cm.
Extent
ix, 105 pages
Isbn
9780821819432
Lccn
99087060
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
System control number
  • (OCoLC)43076813
  • (OCoLC)ocm43076813
Label
Dynamical properties of diffeomorphisms of the annulus and of the torus, Patrice Le Calvez ; translated by Philippe Mazaud
Publication
Bibliography note
Includes bibliographical references (p 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.
Dimensions
25 cm.
Extent
ix, 105 pages
Isbn
9780821819432
Lccn
99087060
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
System control number
  • (OCoLC)43076813
  • (OCoLC)ocm43076813

Library Locations

  • African Studies LibraryBorrow it
    771 Commonwealth Avenue, 6th Floor, Boston, MA, 02215, US
    42.350723 -71.108227
  • Alumni Medical LibraryBorrow it
    72 East Concord Street, Boston, MA, 02118, US
    42.336388 -71.072393
  • Astronomy LibraryBorrow it
    725 Commonwealth Avenue, 6th Floor, Boston, MA, 02445, US
    42.350259 -71.105717
  • Fineman and Pappas Law LibrariesBorrow it
    765 Commonwealth Avenue, Boston, MA, 02215, US
    42.350979 -71.107023
  • Frederick S. Pardee Management LibraryBorrow it
    595 Commonwealth Avenue, Boston, MA, 02215, US
    42.349626 -71.099547
  • Howard Gotlieb Archival Research CenterBorrow it
    771 Commonwealth Avenue, 5th Floor, Boston, MA, 02215, US
    42.350723 -71.108227
  • Mugar Memorial LibraryBorrow it
    771 Commonwealth Avenue, Boston, MA, 02215, US
    42.350723 -71.108227
  • Music LibraryBorrow it
    771 Commonwealth Avenue, 2nd Floor, Boston, MA, 02215, US
    42.350723 -71.108227
  • Pikering Educational Resources LibraryBorrow it
    2 Silber Way, Boston, MA, 02215, US
    42.349804 -71.101425
  • School of Theology LibraryBorrow it
    745 Commonwealth Avenue, 2nd Floor, Boston, MA, 02215, US
    42.350494 -71.107235
  • Science & Engineering LibraryBorrow it
    38 Cummington Mall, Boston, MA, 02215, US
    42.348472 -71.102257
  • Stone Science LibraryBorrow it
    675 Commonwealth Avenue, Boston, MA, 02445, US
    42.350103 -71.103784
Processing Feedback ...