Typical dynamics of volume preserving homeomorphisms / / Steve Alpern, V.S. Prasad [[electronic resource]]

• Record Nr.: UNINA9910450557003321
• Autore: Alpern Steve <1948->
• Pubbl/distr/stampa: Cambridge : , : Cambridge University Press, , 2000
• ISBN: 1-107-12735-1; 1-280-41870-2; 9786610418701; 0-511-17762-3; 0-511-03983-2; 0-511-14803-8; 0-511-30513-3; 0-511-54318-2; 0-511-05400-9
• Descrizione fisica: 1 online resource (xix, 216 pages) : digital, PDF file(s)
• Collana: Cambridge tracts in mathematics ; ; 139
• Disciplina: 514
• Soggetti: Homeomorphisms; Measure-preserving transformations
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Title from publisher's bibliographic system (viewed on 05 Oct 2015).
• Nota di bibliografia: Includes bibliographical references (p. 205-211) and index.
• Nota di contenuto: Volume preserving homeomorphisms of the cube -- Introduction to part I and II (compact manifolds) -- Measure preserving homeomorphisms -- Discrete approximations -- Transitive homeomorphisms of In and Rn -- Fixed points and area preservation -- Measure preserving lusin theorem -- Ergodic homeomorphisms -- Uniform approximation in g[In, delta] and generic properties in M[In, delta] -- Measure preserving homeomorphisms of a compact manifold -- Measures on compact manifolds -- Dynamics on compact manifolds -- Oeasure preserving homeomorphisms of a noncompact manifold -- Ergodic volume preserving homeomorphisms of Rn -- Manifolds where ergodicity is not generic -- Noncompact manifolds and ends -- Ergodic homeomorphisms: the results -- Ergodic homeomorphisms: proofs -- Other properties typical in M[X, u].
• Sommario/riassunto: This 2000 book provides a self-contained introduction to typical properties of homeomorphisms. Examples of properties of homeomorphisms considered include transitivity, chaos and ergodicity. A key idea here is the interrelation between typical properties of volume preserving homeomorphisms and typical properties of volume preserving bijections of the underlying measure space. The authors make the first part of this book very concrete by considering volume preserving homeomorphisms of the unit n-dimensional cube, and they go on to prove fixed point theorems (Conley-Zehnder- Franks). This is done in a number of short self-contained chapters which would be suitable for an undergraduate analysis seminar or a graduate lecture course. Much of this work describes the work of the two authors, over the last twenty years, in extending to different settings and properties, the celebrated result of Oxtoby and Ulam that for volume homeomorphisms of the unit cube, ergodicity is a typical property.