Abstract
In this paper, we are concerned with the existence of invariant curves of reversible mappings. A variant of the classical small twist theorem is given.
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References
Ortega, R.: Boundedness in a piecewise linear oscillator and a variant of the small twist theorem. Proc. London Math. Soc., 79(3), 381–413 (1999)
Ortega, R.: Invariant curves of mappings with averaged small twist. Advanced Nonlinear Studies, 1, 14–39 (2001)
Moser, J.: Convergent series expansions for quasi-periodic motions. Math. Ann., 169, 136–176 (1967)
Moser, J.: Stable and Random Motions in Dynamical Systems, Princeton Univ. Press, N. J., 1973
Sevryuk, M.: Reversible Systems, Lecture Notes in Mathematics, vol. 1211, Springer-Verlag, Berlin, 1986
Pöschel, J.: Integrability of Hamiltonian systems on Cantor sets. Comm. Pure Appl. Math., 34, 653–695 (1982)
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Liu, B., Song, J.J. Invariant Curves of Reversible Mappings with Small Twist. Acta Math Sinica 20, 15–24 (2004). https://doi.org/10.1007/s10114-004-0316-4
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DOI: https://doi.org/10.1007/s10114-004-0316-4