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Hölder Regularity of Grobman–Hartman Theorem for Dynamic Equations on Measure Chains

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Abstract

It has been proven that there exists a one-to-one correspondence H(t, x) between solutions of the linear system and the nonlinear system in the previous work. However, there is no paper considering the Hölder regularity of the transformation H(t, x) in the literature. This paper fills the gap. We establish a strict proof of the Hölder regularity of the transformation H(t, x). We show that the conjugating function H(t, x) in the generalized Hartman–Grobman theorem is always Hölder continuous.

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Acknowledgments

Yonghui Xia was supported by the National Natural Science Foundation of China under Grants (Nos. 11271333 and 10901140), the Natural Science Foundation of Zhejiang Province under Grant (LY15A010007), the Scientific Research Funds of Huaqiao University and China Postdoctoral Science Foundation (No. 2014M562320). Kit Ian Kou was supported from the National Natural Science Foundation of China under Grant (Nos. 11401606 and 11501015), University of Macau (Nos. MYRG2015-00058-FST and MYRG099(Y1-L2)-FST13-KKI) and the Macao Science and Technology Development Fund (No. FDCT/099/2012/A3).

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Authors and Affiliations

  1. School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, Fujian, China

    Yonghui Xia

  2. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Lijun Chen

  3. Department of Mathematics, Faculty of Science and Technology, University of Macau, Macao, China

    Kit Ian Kou

  4. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

    Donal O’Regan

  5. NAAM Research Group, King Abdulaziz University, Jeddah, Saudi Arabia

    Donal O’Regan

Authors
  1. Yonghui Xia
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  2. Lijun Chen
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  3. Kit Ian Kou
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  4. Donal O’Regan
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Correspondence to Yonghui Xia.

Additional information

Communicated by Ahmad Izani Md. Ismail.

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Xia, Y., Chen, L., Kou, K.I. et al. Hölder Regularity of Grobman–Hartman Theorem for Dynamic Equations on Measure Chains. Bull. Malays. Math. Sci. Soc. 41, 1153–1180 (2018). https://doi.org/10.1007/s40840-016-0380-9

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  • DOI: https://doi.org/10.1007/s40840-016-0380-9

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