Rotation theory
نویسنده
چکیده
Rotation Theory has its roots in the theory of rotation numbers for circle homeomorphisms, developed by Poincaré. It is particularly useful for the study and classification of periodic orbits of dynamical systems. It deals with ergodic averages and their limits, not only for almost all points, like in Ergodic Theory, but for all points. We present the general ideas of Rotation Theory and its applications to some classes of dynamical systems, like continuous circle maps homotopic to the identity, torus homeomorphisms homotopic to the identity, subshifts of finite type and continuous interval maps. These notes present a brief survey of some aspects of Rotation Theory. Deeper treatment of the subject would require writing a book. Thus, in particular: • Not all aspects of Rotation Theory are described here. A large part of it, very important and deserving a separate book, deals with homeomorphisms of an annulus, homotopic to the identity. Including this subject in the present notes would make them at least twice as long, so it is ignored, except for the bibliography. • What is called " proofs " are usually only short ideas of the proofs. The reader is advised either to try to fill in the details himself/herself or to find the full proofs in the literature. More complicated proofs are omitted entirely. • The stress is on the theory, not on the history. Therefore, references are not cited in the text. Instead, at the end of these notes there are lists of references dealing with the problems treated in various sections (or not treated at all).
منابع مشابه
Eect of Rotation on Thermoelastic Waves with Green-Naghdi Theory in a Homogeneous Isotropic Hollow Cylinder
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ورودعنوان ژورنال:
- Scholarpedia
دوره 2 شماره
صفحات -
تاریخ انتشار 2007