Chaotic Dynamics of Monotone Twist Maps

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 smoo...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 38; no. 1; pp. 179 - 204
Main Author Yu, Guo Wei
Format Journal Article
LanguageEnglish
Published Beijing Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 2022
Springer Nature B.V
Subjects
Chaos theory
Geodesy
Mathematics
Mathematics and Statistics
Orbits
Riemann manifold
Toruses
Monotone twist maps
homoclinic and heteroclinic orbits
topological entropy
37B40
37E40
37C29
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Summary: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.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-022-0453-7