Rotation Numbers for Random Dynamical Systems on the Circle
نویسندگان
چکیده
In this paper, we study rotation numbers of random dynamical systems on the circle. We prove the existence of rotation numbers and the continuous dependence of rotation numbers on the systems. As an application, we prove a theorem on analytic conjugacy to a circle rotation.
منابع مشابه
A family of rotation numbers for discrete random dynamics on the circle
We revisit the problem of well-defining rotation numbers for discrete random dynamical systems on S. We show that, contrasting with deterministic systems, the topological (i.e. based on Poincaré lifts) approach does depend on the choice of lifts (e.g. continuously for nonatomic randomness). Furthermore, the winding orbit rotation number does not agree with the topological rotation number. Exist...
متن کاملCovering Numbers: Arithmetics and Dynamics for Rotations and Interval Exchanges
We study a particular case of the two-dimensional Steinhaus theorem , giving estimates of the possible distances between points of the form k and k + on the unit circle, through an approximation algorithm of by the points k. This allows us to compute covering numbers (maximal measure of Rokhlin stacks having some prescribed regularity properties) for the symbolic dynamical systems associated to...
متن کاملRotation numbers for quasi-periodically forced monotone circle maps
Rotation numbers have played a central role in the study of (unforced) monotone circle maps. In such a case it is possible to obtain a priori bounds of the form »¡ 1=n μ ...1=n†...yn ¡ y0† μ »‡ 1=n, where ...1=n†...yn ¡ y0† is an estimate of the rotation number obtained from an orbit of length n with initial condition y0, and » is the true rotation number. This allows rotation numbers to be com...
متن کاملRotation number and its properties for iterated function and non-autonomous systems
The main purpose of this paper is to introduce the rotation number for non-autonomous and iterated function systems. First, we define iterated function systems and the lift of these types of systems on the unit circle. In the following, we define the rotation number and investigate the conditions of existence and uniqueness of this number for our systems. Then, the notions rotational entropy an...
متن کاملNeuronal Coding of pacemaker neurons - A random dynamical systems approach
The behaviour of neurons under the influence of periodic external input has been modelled very successfully by circle maps. The aim of this note is to extend certain aspects of this analysis to a much more general class of forcing processes. We apply results on the fibred rotation number of randomly forced circle maps to show the uniqueness of the asymptotic firing frequency of ergodically forc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006