Box dimension of trajectories of some discrete dynamical systems

The Dimension Spectrum of Some Dynamical Systems

We analyze the dimension spectrum previously introduced and measured experimentally by Jensen, Kadanoff, and Libchaber. Using large-deviation theory, we prove, for some invariant measures of expanding Markov maps, that the Hausdorff dimension f(~) of the set on which the measure has a singularity is a well-defined, concave, and regular function. In particular, we show that this is the case for ...

SOME ERGODIC PROPERTIES OF HYPER MV {ALGEBRA DYNAMICAL SYSTEMS

This paper provides a review on major ergodic features of semi-independent hyper MV {algebra dynamical systems. Theorems are presentedto make contribution to calculate the entropy. Particularly, it is proved that thetotal entropy of those semi-independent hyper MV {algebra dynamical systemsthat have a generator can be calculated with respect to their generator ratherthan considering all the par...

study of bifurcation and hyperbolicity in discrete dynamical systems

bifurcations leading to chaos have been investigated in a number of one dimensional dynamical systems by varying the parameters incorporated within the systems. the property hyperbolicity has been studied in detail in each case which has significant characteristic behaviours for regular and chaotic evolutions. in the process, the calculations for invariant set have also been carried out. a bro...

Certifying Trajectories of Dynamical Systems

Some Chaotic Properties of Discrete Fuzzy Dynamical Systems

and Applied Analysis 3 2. Preliminaries In this section, we complete notations and recall some known definitions. Let K X be the class of all nonempty and compact subset of X. If A ∈ K X we define the ε-neighbourhood of A as the set N A, ε {x ∈ X | d x,A < ε}, 2.1 where d x,A infa∈A‖x − a‖. The Hausdorff separation ρ A,B of A,B ∈ K X is defined by ρ A,B inf{ε > 0 | A ⊆ N B, ε }. 2.2 The Hausdor...