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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.

The Research of Sequence Shadowing Property and Regularly Recurrent Point on the Double Inverse Limit Space