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Chaotic Dynamics of Monotone Twist Maps

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Abstract

For a monotone twist map, under certain non-degenerate condition, we showed the existence of infinitely many homoclinic and heteroclinic orbits between two periodic neighboring minimal orbits with the same rotation number, which indicates chaotic dynamics. Our results also apply to geodesics of smooth Riemannian metrics on the two-dimension torus.

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Acknowledgements

The author would like to thank Professor Richard Moeckel for many helpful discussions and useful comments, and Professor Victor Bangert for pointing out the references [8] and [9]. He also thanks the referee for a careful reading of the manuscript and the useful suggestions that helped improving this paper.

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Authors and Affiliations

  1. Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, 300071, P. R. China

    Guo Wei Yu

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  1. Guo Wei Yu
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Correspondence to Guo Wei Yu.

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Supported by National Key R&D Program of China (Grant No. 2020YFA0713303), the Fundamental Research Funds for the Central Universities (Grant No. 63213032) and Nankai Zhide Foundation

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Yu, G.W. Chaotic Dynamics of Monotone Twist Maps. Acta. Math. Sin.-English Ser. 38, 179–204 (2022). https://doi.org/10.1007/s10114-022-0453-7

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  • DOI: https://doi.org/10.1007/s10114-022-0453-7

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