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OverviewThe 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 result 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. This is an English translation of a volume previously published as volume 204 in the Asterisque series. Full Product DetailsAuthor: Patrice Le CalvezPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: No. 4 Weight: 0.226kg ISBN: 9780821819432ISBN 10: 0821819437 Pages: 105 Publication Date: 30 March 2000 Audience: College/higher education , Professional and scholarly , Undergraduate , Postgraduate, Research & Scholarly Format: Paperback Publisher's Status: Active Availability: Out of stock The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsPresentation and comparison of the different approaches to the theory of monotone twist diffeomorphisms of the annulus Generating phases of the diffeomorphisms of the torus and the annulus Index Bibliography.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |