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Lecture III Dynamical systems and turbulence

Part of the Lecture Notes in Mathematics book series (LNM,volume 615)

Keywords

  • Periodic Point
  • Compact Manifold
  • Strange Attractor
  • Closed Orbit
  • Topological Entropy

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Bibliography

  1. Bourbaki, N. Variétés Différentiables, Fascicule des Résultats, §1-8, Hermann, Paris

    Google Scholar 

  2. Bowen, R. Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Mathematics 470, Springer Verlag 1975.

    Google Scholar 

  3. Bowen, R. Topological Entropy and Axiom A, Proc. Symp. Pure Math., vol. 14, Amer. Math. Soc. Providence R.I. 1970, pp. 23–41.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Bowen, R., Ruelle, D. The Ergodic Theory of Axiom A Flows, Inventiones Math., 29 (1975) pp. 181–202.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Hirsch, M. Differential Topology, Graduate Texts in Mathematics 33, Springer Verlag 1975.

    Google Scholar 

  6. Hirsch, M., Smale, S. Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press, 1974.

    Google Scholar 

  7. Hirsch, M., Pugh, C. Stable Manifolds and Hyperbolic Sets, Proc. Symp. Pure Math. 14 (1970), 133–163.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Palis, J., deMelo, W. Introdução aos Sistemas Dinâmicos, Colóquio Brasileiro de Matematica Pocos de Coldas, Julho 1975, IMPA.

    Google Scholar 

  9. Robbin, J. Topological Conjugacy and Structural Stability for Discrete Dynamical Systems, BAMS, vol. 78, No. 6, November 1972, pp. 923–952.

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Smale, S. Differentiable Synamical Systems, B.A.M.S. 73 (1967) pp. 797–817.

    MathSciNet  Google Scholar 

  12. Shub, M. Stability in Dynamical Systems, (preprint).

    Google Scholar 

  13. Shub, M. Dynamical Systems, Filtrations and Entropy, B.A.M.S. vol. 80, No. 1, January 1974, pp. 27–41.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. Walters, P. Ergodic Theory — Introductory Lectures, Lecture Notes in Mathematics 458, Springer Verlag, 1975.

    Google Scholar 

  15. Williams, R. Expanding Attractors, Publications Mathematiques, no. 43, I HES, 1974.

    Google Scholar 

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© 1977 Springer-Verlag

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Smale, S. (1977). Lecture III Dynamical systems and turbulence. In: Bernard, P., Ratiu, T. (eds) Turbulence Seminar. Lecture Notes in Mathematics, vol 615. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0068360

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  • DOI: https://doi.org/10.1007/BFb0068360

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08445-7

  • Online ISBN: 978-3-540-37074-1

  • eBook Packages: Springer Book Archive