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Smooth transformations of intervals

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Séminaire Bourbaki vol. 1980/81 Exposés 561–578

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 901))

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References

  1. M. Campanino, H. Epstein, and D. Ruelle, “On Feigenbaum's functional equation”, IHES preprint P/80/32 (1980). M. Campanino and H. Epstein, “On the existence of Feigenbaum's fixed point”, IHES preprint P/80/35 (1980).

    Google Scholar 

  2. P. Collet and J.-P. Eckmann, “Iterated Maps on the Interval as Dynamical Systems”, Birkhäuser, Boston-Basel-Stuttgart, 1980.

    MATH  Google Scholar 

  3. P. Collet, J.-P. Eckmann, and O. E. Lanford, “Universal properties of maps on an interval”, Commun. Math. Phys. 76 (1980) 211–254.

    Article  MATH  MathSciNet  Google Scholar 

  4. M. Feigenbaum, “Quantitative universality for a class of non-linear transformations”, J. Stat. Phys. 19 (1978) 25–52. “The universal metric properties of non-linear transformation”, J. Stat. Phys. 21 (1979) 669–706.

    Article  MATH  MathSciNet  Google Scholar 

  5. J. Guckenheimer, “Bifurcations of maps of the interval”, Inventiones Math. 39 (1977) 165–178.

    Article  MATH  MathSciNet  Google Scholar 

  6. J. Guckenheimer, “Sensitive dependence on initial conditions for one dimensional maps”, Commun. Math. Phys. 70 (1979) 133–160.

    Article  MATH  MathSciNet  Google Scholar 

  7. E. N. Lorenz, “On the prevalence of aperiodicity for simple systems”, Springer Lecture Notes in Mathematics 755 (1979) 53–77.

    Article  MATH  MathSciNet  Google Scholar 

  8. R. B. May, “Simple mathematical models with very complicated dynamics”, Nature 261 (1976) 459–467.

    Article  Google Scholar 

  9. M. Metropolis, M. L. Stein, and P. R. Stein, “On finite limit sets for transformations of the unit interval”, J. Combinatorial Theory 15 (1973) 25–44.

    Article  MATH  MathSciNet  Google Scholar 

  10. M. Misiurewicz, “Absolutely continuous measures for certain maps of an interval”, IHES preprint, M/79/293 (1979).

    Google Scholar 

  11. D. Singer, “Stable orbits and bifurcations of maps of the interval”, SIAM J. Appl. Math. 35 (1978) 260–267.

    Article  MATH  MathSciNet  Google Scholar 

  12. P. Coullet and J. Tresser, “Itérations d'endomorphismes et groupe de renormalisation”, C. R. Acad. Sci., Paris 287 (1978) 577–580. “Itérations d'endomorphismes et groupe de renormalisation”, Journal de Physique 39 (1978) C5-25–C5-28.

    MATH  MathSciNet  Google Scholar 

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© 1981 N. Bourbaki

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Lanford, O.E. (1981). Smooth transformations of intervals. In: Séminaire Bourbaki vol. 1980/81 Exposés 561–578. Lecture Notes in Mathematics, vol 901. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0097188

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  • DOI: https://doi.org/10.1007/BFb0097188

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11176-4

  • Online ISBN: 978-3-540-38956-9

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