The hyperbolic invariant tori of symplectic mappings

The hyperbolic invariant tori of symplectic mappings

In this paper we study the persistence of lower dimensional hyperbolic invariant tori for nearly integrable twist symplectic mappings. Under a Rüssmann-type non-degenerate condition, by introducing a modified KAM iteration scheme, we proved that nearly integrable twist symplectic mappings admit a fa...

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Veröffentlicht in:Nonlinear analysis 2008, Vol.68 (1), p.109-126
Hauptverfasser: Zhu, Wenzhuang, Liu, Baifeng, Liu, Zhenxin
Format: Artikel
Sprache:eng
Schlagworte:
Exact sciences and technology
Invariant tori
KAM theorem
Mathematical analysis
Mathematics
Sciences and techniques of general use
Symplectic mappings
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Zusammenfassung:In this paper we study the persistence of lower dimensional hyperbolic invariant tori for nearly integrable twist symplectic mappings. Under a Rüssmann-type non-degenerate condition, by introducing a modified KAM iteration scheme, we proved that nearly integrable twist symplectic mappings admit a family of lower dimensional hyperbolic invariant tori as long as the symplectic perturbation is small enough.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2006.10.035