Linear Diffeomorphisms With Limit Shadowing

This paper proves that the linear transformation [Formula: see text] on [Formula: see text] has the (asymptotic) average shadowing property if and only if [Formula: see text] is hyperbolic, where [Formula: see text] is a nonsingular matrix, giving a positive answer to a question in [Lee, 2012a]. Besides, it is proved that [Formula: see text] does not have the [Formula: see text]-shadowing property, thus does not have the ergodic shadowing property for every nonsingular matrix [Formula: see text].

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Linear Diffeomorphisms With Limit Shadowing

Cited by 2 publications

References 2 publications

Shadowing, limit shadowing and two-sided limit shadowing

Shadowing, limit shadowing and two-sided limit shadowing

Various Shadowing in Linear Dynamical Systems

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