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Diffeomorphisms with a generalized Lipschitz shadowing property

  • * Corresponding author: Xiao Wen

    * Corresponding author: Xiao Wen
M. Lee was supported by NRF-2017R1A2B4001892 and NRF-2020R1F1A1A01051370. J. Oh was supported by NRF-2019R1A2C1002150. X. Wen was supported by National Natural Science Foundation of China (No. 11671025 and No. 11571188) and Fundamental Research Funds for the Central Universities
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  • Shadowing property and structural stability are important dynamics with close relationship. Pilyugin and Tikhomirov proved that Lipschitz shadowing property implies the structural stability[5]. Todorov gave a similar result that Lipschitz two-sided limit shadowing property also implies structural stability for diffeomorpshisms[10]. In this paper, we define a generalized Lipschitz shadowing property which unifies these two kinds of Lipschitz shadowing properties, and prove that if a diffeomorphism $ f $ of a compact smooth manifold $ M $ has this generalized Lipschitz shadowing property then it is structurally stable. The only if part is also considered.

    Mathematics Subject Classification: Primary: 37C20, 37C05, 37D05.


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