In this paper we give conditions for a tuple of commutative bounded linear operators which holds in the property of the Hypercyclicity Criterion. We characterize topological transitivity and semi-hereiditarily of a dynamical system given  by an n-tuple of operators acting on a separable infinite dimensional Banach space .

in this paper, we introduce a notion of property (t) for a c∗-dynamical system (a, g, α) consisting of a unital c∗-algebra a,a locally compact group g, and an action α on a. as a result,we show that if a has strong property (t) and g has kazhdan’sproperty (t), then the triple (a, g, α) has property (t).

in this paper we give conditions for a tuple of commutative bounded linear operators which holds in the property of the hypercyclicity criterion. we characterize topological transitivity and semi-hereiditarily of a dynamical system given  by an n-tuple of operators acting on a separable infinite dimensional banach space .

Some characterizations on the chain recurrence, chain transitivity, chain mixing property,shadowing and $h$-shadowing for Zadeh's extension are obtained. Besides, it is provedthat a dynamical system is spatiotemporally chaotic provided that the Zadeh's extensionis Li-Yorke sensitive.

In this paper, first the space of hyperbolic tangent functions is introduced and then the universal approximator property of this space is proved. In fact, by using this space, any nonlinear continuous function can be uniformly approximated with any degree of accuracy. Also, as an application, this space of functions is utilized to design feedback control for a nonlinear dynamical system.

In this paper, we introduce a notion of property (T) for a C<span style="font-family: txsy; font-size: 7pt; color: #000000; font-style: norm...

In this paper we study shadowing property for sequences of mappings on compact metric spaces, i.e. nonautonomous discrete dynamical systems. We investigate the relation of  weak contractions with shadowing and h-shadowing property.

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 ...

in this paper we introduce the concept of entropy operator for continuous systems of finite topological entropy. it is shown that it generates the kolmogorov entropy as a special case. if $phi$ is invertible then the entropy operator is bounded with the topological entropy of $phi$ as its norm.

The repetition property of a dynamical system, a notion introduced in [2], plays an importance role in analyzing spectral properties of ergodic Schrödinger operators. In this paper, entropy of dynamical systems with repetition property is investigated. It is shown that the topological entropy of dynamical systems with the global repetition property is zero. Minimal dynamical systems having both...