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• catalog abstract ""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.".
• catalog alternative "Propriétés dynamiques des difféomorphismes de l'anneau et du tore. English".
• catalog contributor b11812736.
• catalog created "2000.".
• catalog date "2000".
• catalog date "2000.".
• catalog dateCopyrighted "2000.".
• catalog description ""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."".
• catalog description ""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.".
• catalog description "Ch. 1. 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. 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. 2.2. Composition of twist diffeomorphisms of the plane. 2.3. Existence of orbits with trivial braid type for conservative diffeomorphisms of the annulus.".
• catalog description "Includes bibliographical references (p 101-105) and index.".
• catalog extent "ix, 105 p. :".
• catalog identifier "0821819437".
• catalog isPartOf "SMF/AMS texts and monographs ; v. 4".
• catalog issued "2000".
• catalog issued "2000.".
• catalog language "eng fre".
• catalog language "eng".
• catalog publisher "Providence, RI : American Mathematical Society,".
• catalog subject "514/.74 21".
• catalog subject "Diffeomorphisms.".
• catalog subject "Differentiable dynamical systems.".
• catalog subject "Mappings (Mathematics)".
• catalog subject "QA613.65 .L4213 2000".
• catalog tableOfContents "Ch. 1. 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. 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. 2.2. Composition of twist diffeomorphisms of the plane. 2.3. Existence of orbits with trivial braid type for conservative diffeomorphisms of the annulus.".
• catalog title "Dynamical properties of diffeomorphisms of the annulus and of the torus / Patrice Le Calvez ; translated by Philippe Mazaud.".
• catalog title "Propriétés dynamiques des difféomorphismes de l'anneau et du tore. English".
• catalog type "text".