Let (E,h1,∞) be a nonautonomous discrete dynamical system (briefly, N.D.D.S.) that is defined by sequence (hj)j=1∞ of continuous maps hj:E→E over nontrivial metric space (E,d). This paper defines and discusses some forms ergodicity sensitivity for the upper density, lower positive integers. Under conditions, if rate convergence at which converges to limit map h “fast enough” with respect intege...

This paper is devoted to the construction of an energy function, i.e. a smooth Lyapunov whose set critical points coincides with chain-recurrent dynamical system — for cascade that direct product two systems. One multipliers structurally stable diffeomorphism given on two-dimensional torus, non-wandering consists zero-dimensional non-trivial basic without pairs conjugated and fixed source sink,...

We generalize the study of symbolic dynamical systems of nite type and ZZ 2 action, and the associated use of symbolic substitution dynamical systems, to dynamical systems with IR 2 action. The new systems are associated with tilings of the plane. We generalize the classical technique of the matrix of a substitution to include the geometrical information needed to study tilings, and we utilize ...