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Shadowing and Inverse Shadowing for C 1 Endomorphisms

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Abstract

In this paper, we consider the shadowing and the inverse shadowing properties for C 1 endomorphisms. We show that near a hyperbolic set a C 1 endomorphism has the shadowing property, and a hyperbolic endomorphism has the inverse shadowing property with respect to a class of continuous methods. Moreover, each of these shadowing properties is also “uniform” with respect to C 1 perturbation.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050016, P. R. China

    Yu Jun Zhu

  2. School of Mathematical Sciences, Peking University, Bejing 100871, P. R. China

    Yu Jun Zhu

  3. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050016, P. R. China

    Jin Lian Zhang & Lian Fa He

Authors
  1. Yu Jun Zhu
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  2. Jin Lian Zhang
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  3. Lian Fa He
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Correspondence to Yu Jun Zhu.

Additional information

Research supported by the National Natural Science Foundation of China (10371030), the Tian Yuan Mathematical Foundation of China (10426012) and the Doctoral Foundation of Hebei Normal University (L2003B05)

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Zhu, Y.J., Zhang, J.L. & He, L.F. Shadowing and Inverse Shadowing for C 1 Endomorphisms. Acta Math Sinica 22, 1321–1328 (2006). https://doi.org/10.1007/s10114-005-0739-6

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  • DOI: https://doi.org/10.1007/s10114-005-0739-6

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