Topological transitivity
نویسندگان
چکیده
The concept of topological transitivity goes back to G. D. Birkhoff [1]
منابع مشابه
Chaotic property for non-autonomous iterated function system
In this paper, the new concept of non-autonomous iterated function system is introduced and also shown that non-autonomous iterated function system IFS(f_(1,∞)^0,f_(1,∞)^1) is topologically transitive for the metric space of X whenever the system has average shadowing property and its minimal points on X are dense. Moreover, such a system is topologically transitive, whenever, there is a point ...
متن کاملTransitivity of Euclidean Extensions of Anosov Diffeomorphisms
We consider the class of Rn extensions of Anosov diffeomorphisms on infranilmanifolds, and find necessary and sufficient conditions for topological transitivity. In particular, if the fiber is R, the existence of a semi-orbit with the projection on R unbounded from above and from below is equivalent to topological transitivity. We also show that in the above class topological transitivity and s...
متن کاملTopological Transitivity and Strong Transitivity
We discuss the relation between (topological) transitivity and strong transitivity of dynamical systems. We show that a transitive and open self-map of a compact metric space satisfying a certain expanding condition is strongly transitive. We also prove a couple of results for interval maps; for example it is shown that a transitive piecewise monotone interval map is strongly transitive.
متن کاملTransitivity and Chaoticity in 1-D Cellular Automata
Recent progress in symbolic dynamics of cellular automata (CA) shows that many CA exhibit rich and complicated Bernoulli-shift properties, such as positive topological entropy, topological transitivity and even mixing. Noticeably, some CA are only transitive, but not mixing on their subsystems. Yet, for one-dimensional CA, this paper proves that not only the shift transitivity guarantees the CA...
متن کاملA survey on transitivity in discrete time dynamical systems. application to symbolic systems and related languages
The main goal of this paper is the investigation of a relevant property which appears in the various definition of deterministic topological chaos for discrete time dynamical system: transitivity. Starting from the standard Devaney’s notion of topological chaos based on regularity, transitivity, and sensitivity to the initial conditions, the critique formulated by Knudsen is taken into account ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Scholarpedia
دوره 4 شماره
صفحات -
تاریخ انتشار 2009