Typical Dynamics Of Volume Preserving Homeomorphisms
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Author | : Steve Alpern |
Publisher | : Cambridge University Press |
Total Pages | : 238 |
Release | : 2001-03-29 |
Genre | : Mathematics |
ISBN | : 1139433202 |
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.
Author | : Katsuhiro Shiohama |
Publisher | : Cambridge University Press |
Total Pages | : 300 |
Release | : 2003-11-13 |
Genre | : Mathematics |
ISBN | : 9780521450546 |
This is a self-contained account of how some modern ideas in differential geometry can be used to tackle and extend classical results in integral geometry. The authors investigate the influence of total curvature on the metric structure of complete, non-compact Riemannian 2-manifolds, though their work, much of which has never appeared in book form before, can be extended to more general spaces. Many classical results are introduced and then extended by the authors. The compactification of complete open surfaces is discussed, as are Busemann functions for rays. Open problems are provided in each chapter, and the text is richly illustrated with figures designed to help the reader understand the subject matter and get intuitive ideas about the subject. The treatment is self-contained, assuming only a basic knowledge of manifold theory, so is suitable for graduate students and non-specialists who seek an introduction to this modern area of differential geometry.
Author | : I. G. Macdonald |
Publisher | : Cambridge University Press |
Total Pages | : 200 |
Release | : 2003-03-20 |
Genre | : Mathematics |
ISBN | : 9780521824729 |
First account of a theory, created by Macdonald, of a class of orthogonal polynomial, which is related to mathematical physics.
Author | : Claus Hertling |
Publisher | : Cambridge University Press |
Total Pages | : 292 |
Release | : 2002-07-25 |
Genre | : Mathematics |
ISBN | : 9780521812962 |
This book presents the theory of Frobenius manifolds, as well as all the necessary tools and several applications.
Author | : American Mathematical Society |
Publisher | : |
Total Pages | : 678 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : |
Author | : Joseph Auslander |
Publisher | : American Mathematical Soc. |
Total Pages | : 336 |
Release | : 2016-11-29 |
Genre | : Mathematics |
ISBN | : 1470422999 |
This volume contains the proceedings of three conferences in Ergodic Theory and Symbolic Dynamics: the Oxtoby Centennial Conference, held from October 30–31, 2010, at Bryn Mawr College; the Williams Ergodic Theory Conference, held from July 27–29, 2012, at Williams College; and the AMS Special Session on Ergodic Theory and Symbolic Dynamics, held from January 17–18, 2014, in Baltimore, MD. This volume contains articles covering a variety of topics in measurable, symbolic and complex dynamics. It also includes a survey article on the life and work of John Oxtoby, providing a source of information about the many ways Oxtoby's work influenced mathematical thought in this and other fields.
Author | : |
Publisher | : |
Total Pages | : 904 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : |
Author | : S. F. Koli︠a︡da |
Publisher | : American Mathematical Soc. |
Total Pages | : 378 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : 0821837516 |
This volume contains a collection of articles from the special program on algebraic and topological dynamics and a workshop on dynamical systems held at the Max-Planck Institute (Bonn, Germany). It reflects the extraordinary vitality of dynamical systems in its interaction with a broad range of mathematical subjects. Topics covered in the book include asymptotic geometric analysis, transformation groups, arithmetic dynamics, complex dynamics, symbolic dynamics, statisticalproperties of dynamical systems, and the theory of entropy and chaos. The book is suitable for graduate students and researchers interested in dynamical systems.
Author | : |
Publisher | : |
Total Pages | : 530 |
Release | : 2006 |
Genre | : Differentiable dynamical systems |
ISBN | : |
Author | : Vladimir I. Bogachev |
Publisher | : Springer Science & Business Media |
Total Pages | : 1075 |
Release | : 2007-01-15 |
Genre | : Mathematics |
ISBN | : 3540345140 |
This book giving an exposition of the foundations of modern measure theory offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course, and, finally, more specialized topics partly covered by more than 850 exercises with detailed hints and references. Bibliographical comments and an extensive bibliography with 2000 works covering more than a century are provided.