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Existence of infinite non-Birkoff periodic orbits for area-preserving monotone twist maps of cylinders

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Abstract

The exact monotone twist map of infinite cylinders in the Birkhoff region of instability is studied. A variational method based on Aubry-Mather theory is used to discover infinitely many non-Birkhoff periodic orbits of fixed rotation number sufficiently close to some irrational number for which the angular invariant circle does not exist.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, 210093, Nanjing, China

    Wei Cheng & Chongqing Cheng

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  1. Wei Cheng
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  2. Chongqing Cheng
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Cheng, W., Cheng, C. Existence of infinite non-Birkoff periodic orbits for area-preserving monotone twist maps of cylinders. Sci. China Ser. A-Math. 43, 810–817 (2000). https://doi.org/10.1007/BF02884180

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  • DOI: https://doi.org/10.1007/BF02884180

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