A topological shadowing theorem
Tóm tắt
We prove a topological version of the classical shadowing theorem in differentiable dynamics (Encyclopedia of Mathematics and its Applications, vol. 54 (1995) (Cambridge: Cambridge University Press)). We use it to unify some stability results in literature as the GH-topological, Hartman and Walters stability theorems Discrete Contin. Dyn. Syst. 37(7) (2017) 3531–3544; An. Acad. Brasil Ci. 40 (1968) 263–266; Am. J. Math. 91 (1969) 363–367; Proceedings of Conference, North Dakota State University, Fargo, N.D., 1977 (1978) (Berlin: Springer) pp. 231–244).
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