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Bifurcation of periodic solutions into invariant tori: The work of Ruelle and Takens

Part of the Lecture Notes in Mathematics book series (LNM,volume 322)

Keywords

  • Banach Space
  • Periodic Solution
  • Unit Circle
  • Spectral Radius
  • Invariant Manifold

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References

  1. Bonic, R. and Frampton, J., Smooth Functions on Banach Manifolds, J. Math. Mech. 15 (1966), 877–898.

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  2. Dunford, H., and Schwartz, J.T., Linear Operators I. New York: Interscience, 1958.

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  3. Kelley, A., The Stable, Center-Stable, Center, Center-Unstable, and Unstable Manifolds; Appendix C of R. Abraham and J. Robbins, Transversal Mappings and Flows. New York: W. A. Benjamin, 1967.

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  4. Ruelle, D. and Takens, F., On the Nature of Turbulence, Commun. Math. Phys. 20 (1971), 167–192.

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  5. , Note Concerning our Paper "On the Nature of Turbulence", Comm. Math. Phys. 23 (1971), 343–344.

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  6. Siegel, C. L. and Moser, J. K., Lectures on Celestial Mechanics. Berlin, Heidelberg, New York: Springer-Verlag, 1971.

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© 1973 Springer Verlag

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Lanford, O.E. (1973). Bifurcation of periodic solutions into invariant tori: The work of Ruelle and Takens. In: Stakgold, I., Joseph, D.D., Sattinger, D.H. (eds) Nonlinear Problems in the Physical Sciences and Biology. Lecture Notes in Mathematics, vol 322. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060566

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  • DOI: https://doi.org/10.1007/BFb0060566

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06251-6

  • Online ISBN: 978-3-540-38558-5

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