On Attractor and Pseudo Orbit Tracing of Uniform Limit Dynamical Systems

Abstract

ABSTRACT Some dynamical properties of the uniform limit dynamical system have been investigated. It has been found that for a sequences (X, Fn) of dynamical systems having same attractor A and converging uniformly to a dynamical system (X, f), the dynamical system (X, f) has the same attractor A. It has been found that a sequence (X, Fn) of uniformly rigid dynamical systems converging uniformly to a dynamical system (X, f), the dynamical system (X, f) is also uniformly rigid. We have proved that the uniform limit (X, f) of a uniformly convergent sequence of dynamical systems having pseudo orbit tracing property has pseudo orbit tracing property. The expansiveness and the equicontinuous set ϵ: of the uniform limit dynamical system have been investigated.