Abstract
According to the definition of sequence shadowing property and regularly recurrent point in the inverse limit space, we introduce the concept of sequence shadowing property and regularly recurrent point in the double inverse limit space and study their dynamical properties. The following results are obtained: (1) Regularly recurrent point sets of the double shift map σ f ∘ σ g are equal to the double inverse limit space of the double self-map f ∘ g in the regularly recurrent point sets. (2) The double self-map f ∘ g has sequence shadowing property if and only if the double shift map σ f ∘ σ g has sequence shadowing property. Thus, the conclusions of sequence shadowing property and regularly recurrent point are generalized to the double inverse limit space.
Highlights
The conclusions of sequence shadowing property and regularly recurrent point are generalized to the double inverse limit space
Inverse limit space plays an important role in topological dynamical systems, and a series of research results have been obtained
The new concepts of sequence shadowing property and regularly recurrent point are given in double inverse limit space
Summary
Inverse limit space plays an important role in topological dynamical systems, and a series of research results have been obtained (see [1,2,3,4]). It is known that shadowing property and regularly recurrent point have always been the focus of topological dynamical systems. Many scholars have studied them in the inverse limit space and obtained valuable research results (see [9,10,11,12,13,14,15]). The new concepts of sequence shadowing property and regularly recurrent point are given in double inverse limit space. The results enrich the conclusions of sequence shadowing property and regularly recurrent point in the double inverse limit space
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