Expectations over Attractors of Iterated Function Systems

نویسندگان

  • JONATHAN M. BORWEIN
  • MICHAEL G. ROSE
چکیده

Motivated by the need for new mathematical tools applicable to the study of fractal point-cloud distributions, expectations of complex-valued functions defined over general ‘deterministic’ fractal domains are considered, following the development of a measure-theoretic foundation for their analysis. In particular, we wish to understand and evaluate separation moments as given by integrals of the form

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Connectedness of the Attractors of Iterated Function Systems

We survey some of the topological properties of the attractors of iterated function systems such as connectedness, arcwise connectedness and locally arcwise connectedness. We give necessary and sufficient conditions for the attractors of finite iterated function system (IFS) to be a connected sets and in the case when infinite iterated function systems (IIFS) are considered we give only some su...

متن کامل

Minimal attractors and bifurcations of random dynamical systems

We consider attractors for certain types of random dynamical systems. These are skew-product systems whose base transformations preserve an ergodic invariant measure. We discuss definitions of invariant sets, attractors and invariant measures for deterministic and random dynamical systems. Under assumptions that include, for example, iterated function systems, but that exclude stochastic differ...

متن کامل

Rotation 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 کامل

Discrete Iterated Function Systems

discrete iterated function systems discrete iterated function systems representation of discrete sequences with dimensional discrete iterated function systems discrete iterated function systems stochastic discrete scale invariance: renormalization representation of discrete sequences with high-dimensional power domains and iterated function systems fractal tilings from iterated function systems...

متن کامل

Attractors of Iterated Function Systems

In this paper, the question of which compact metric spaces can be attractors of hyperbolic iterated function systems on Euclidean space is studied. It is shown that given any finite-dimensional compact metric X , there is a Cantor set C such that the disjoint union of C and X is an attractor. In the process, it is proved that every such X is the Lipschitz image of a Cantor set.

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2015