Abstract
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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Acknowledgements
The first author was partially supported by Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education (NRF-2019R1A6A3A01091340). The second author was partially supported by CNPq-Brazil and the NRF Brain Pool Grant, funded by the Korea Government No. 2020H1D3A2A01085417.
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Communicated by Mahan Mj.
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Lee, J., Rojas, A. A topological shadowing theorem. Proc Math Sci 132, 32 (2022). https://doi.org/10.1007/s12044-022-00675-6
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DOI: https://doi.org/10.1007/s12044-022-00675-6