Sensitivity of iterated function systems

  title={Sensitivity of iterated function systems},
  author={Fatemeh Helen Ghane and E. Rezaali and Ali Sarizadeh},
  journal={Journal of Mathematical Analysis and Applications},

On Equicontinuity, Transitivity and Distality of Iterated Function Systems

Abstract In this paper, equicontinuity, transitivity, minimality, sensitivity, and distality of iterated function systems(IFS) have been discussed. The equicontinuity, almost equicontinuity, and

Hypercyclic operators for iterated function systems

In this paper we introduce and study the notion of hypercyclicity for iterated function systems (IFS) of operators. We prove that for a linear IFS, hypercyclicity implies sensitivity and if an IFS is

A Remark on Sensitivity and Li–Yorke Sensitivity of Iterated Function Systems

This considers how sensitivity and Li–Yorke sensitivity on iterated function systems carry over to their products and proves that the sensitivity and Li–Yorke sensitivity are both preserved under

A Simple Proof of a Theorem of Sensitivity

We prove that every transitive and non-minimal semigroup with dense minimal points is sensitive. When the system is almost open, we obtain a generalization of this result.

Chaotic iterated function systems

Transitivity and sensitivity of iterated function systems via Furstenberg families

In this paper, we study variants of transitivity and sensitivity via Furstenberg families for iterated function systems (IFSs). Using the concept of skew product transformation of an IFS, we obtain



A note on sensitivity of semigroup actions

Abstract It is well known that for a transitive dynamical system (X,f) sensitivity to initial conditions follows from the assumption that the periodic points are dense. This was done by several

Residual properties and almost equicontinuity

A propertyP of a compact dynamical system (X,f) is called a residual property if it is inherited by factors, almost one-to-one lifts and surjective inverse limits. Many transitivity properties are

Stronger forms of sensitivity for dynamical systems

For continuous self-maps of compact metric spaces, we initiate a preliminary study of stronger forms of sensitivity formulated in terms of ‘large’ subsets of . Mainly we consider ‘syndetic

Sensitive dependence on initial conditions

It is shown that the property of sensitive dependence on initial conditions in the sense of Guckenheimer follows from the other two more technical parts of one of the most common recent definitions

Li-Yorke sensitivity

We introduce and study a concept which links the Li–Yorke versions of chaos with the notion of sensitivity to initial conditions. We say that a dynamical system (X,T) is Li–Yorke sensitive if there

The sufficient conditions for dynamical systems of semigroup actions to have some stronger forms of sensitivities

In this paper, we introduce several stronger forms of sensitivities in the dynamical systems of semigroup actions, such as thick sensitivity and thickly syndetical sensitivity, and obtain some

Hereditarily non-sensitive dynamical systems and linear representations

For an arbitrary topological group G any compact G-dynamical system (G, X) can be linearly G-represented as a weak∗-compact subset of a dual Banach space V ∗. As was shown in [45] the Banach space V

On the chaos game of Iterated Function Systems

Every quasi-attractor of an iterated function system (IFS) of continuous functions on a first-countable Hausdorff topological space is renderable by the probabilistic chaos game. By contrast, we

On Devaney's definition of chaos

Chaotic dynamical systems have received a great deal of attention in recent years (see for instance [2], [3]). Although there has been no universally accepted mathematical definition of chaos, the