Abstract:
We show that a generic area-preserving two-dimensional map with an elliptic periodic point is Cω-universal, i.e., its renormalized iterates are dense in the set of all real-analytic symplectic maps of a two-dimensional disk. The results naturally extend onto Hamiltonian and volume-preserving flows.
Keywords:
homoclinic tangency, wild hyperbolic set, Newhouse phenomenon, Hamiltonian system, area-preserving map, volume-preserving flow, exponentially small splitting, KAM theory.
Citation:
V. Gelfreich, D. Turaev, “Universal dynamics in a neighborhood of a generic elliptic periodic point”, Regul. Chaotic Dyn., 15:2-3 (2010), 159–164
\Bibitem{GelTur10}
\by V. Gelfreich, D. Turaev
\paper Universal dynamics in a neighborhood of a generic elliptic periodic point
\jour Regul. Chaotic Dyn.
\yr 2010
\vol 15
\issue 2-3
\pages 159--164
\mathnet{http://mi.mathnet.ru/rcd485}
\crossref{https://doi.org/10.1134/S156035471002005X}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2644327}
\zmath{https://zbmath.org/?q=an:1203.37100}
Linking options:
https://www.mathnet.ru/eng/rcd485
https://www.mathnet.ru/eng/rcd/v15/i2/p159
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