Nonautonomous attractors and Young measures

Motivated by the problem of identifying a mathematical framework for the formal definition of concepts such as weather, climate and connections between them, we discuss a question of convergence of short-time time averages for random nonautonomous dynamical systems depending on a parameter. The problem is formulated by means of Young measures. Using the notion of pull-back attractor, we prove a general theorem giving a sufficient condition for the tightness of the law of the approximating problems. In a specific example, we show that the theorem applies and we characterize the unique limit point.

A Note on Variational Principle of Subsets for Nonautonomous Dynamical Systems

In this paper, we introduce measure-theoretic for Borel probability measures to characterize upper and lower Katok measure-theoretic entropies in discrete type and the measure-theoretic entropy for arbitrary Borel probability measure in nonautonomous case. Then we establish new variational principles for Bowen topological entropy for nonautonomous dynamical systems. JEL classification numbers: 37A35. Keywords: Nonautonomous, Measure-theoretical entropies, Variational principles.

Sensitivity of Nonautonomous Dynamical Systems on Uniform Spaces

We introduce the concepts of sensitivity, multisensitivity, cofinite sensitivity, and syndetic sensitivity for nonautonomous dynamical systems on uniform spaces and obtain some sufficient conditions under which topological transitivity and dense periodic points imply sensitivity for nonautonomous systems on Hausdorff uniform spaces. We also study sensitivity and other stronger versions of sensitivity for the systems induced on hyperspaces and for the product of nonautonomous dynamical systems on uniform spaces.

On some kinds of dense orbits in general nonautonomous dynamical systems

We study the theory of universality for the nonautonomous dynamical systems from topological point of view related to hypercyclicity. The conditions are provided in a way that Birkhoff transitivity theorem can be extended. In the context of generalized linear nonautonomous systems, we show that either one of the topological transitivity or hypercyclicity give sensitive dependence on initial conditions. Meanwhile, some examples are presented for topological transitivity, hypercyclicity and topological conjugacy.