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Hamiltonian Dynamical Systems pp 373–385Cite as

Existence of Invariant Tori for Certain Non-Symplectic Diffeomorphisms

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Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 63))

Abstract

In this paper, we consider certain diffeomorphisms on I m × T n, where I = [1, 2] ⊂ ℝ and T = S 1 . We show that under certain nondegeneracy conditions and intersection property, all of the maps sufficiently close to the integrable ones preserve a large set of m-dimensional invariant tori. Some applications of these results to forced oscillations with changing forcing frequencies are given.

School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332. Research supported in part by the National Science Foundation.

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References

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Author information

Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Zhihong Xia

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  1. Zhihong Xia
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Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, University of Cincinnati, 45221, Cincinnati, OH, USA

    H. S. Dumas

  2. Institute for Dynamics Department of Mathematical Sciences, University of Cincinnati, 45221, Cincinnati, OH, USA

    K. S. Meyer

  3. Department of Computer Science, University of Cincinnati, 45221, Cincinnati, OH, USA

    D. S. Schmidt

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© 1995 Springer-Verlag New York, Inc.

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Xia, Z. (1995). Existence of Invariant Tori for Certain Non-Symplectic Diffeomorphisms. In: Dumas, H.S., Meyer, K.S., Schmidt, D.S. (eds) Hamiltonian Dynamical Systems. The IMA Volumes in Mathematics and its Applications, vol 63. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8448-9_25

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  • DOI: https://doi.org/10.1007/978-1-4613-8448-9_25

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8450-2

  • Online ISBN: 978-1-4613-8448-9

  • eBook Packages: Springer Book Archive

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