Properties of continuous maps of the interval to itself

  • P. Collet
  • J. -P. Eckman
Dynamical Systems Session Organized by D. Ruelle
Part of the Lecture Notes in Physics book series (LNP, volume 116)


Periodic Point Unstable Manifold Stable Period Schwarzian Derivative Sensitive Dependence 
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  1. D. Singer. Stable orbits and bifurcations of maps on the interval. SIAM J. Appl. Math. 35, 260 (1978).Google Scholar
  2. M. Misiurewicz. Absolutely continuous measures for certain maps of an interval. Preprint IHES, Bures-sur-Yvette (1979).Google Scholar
  3. D. Ruelle. Applications conservant une mesure absolument continue par rapport à dx sur [0,1]. Commun. Math. Phys. 55, 47 (1977).Google Scholar
  4. P. Collet, J.-P. Eckmann. Abundance of chaotic behaviour for maps on the interval. Preprint. University of Geneva (1979).Google Scholar
  5. J. Milnor, W. Thurston. On iterated maps of the interval I, II. Preprint, Princeton (1977).Google Scholar
  6. J. Guckenheimer. Sensitive dependence to initial conditions for one dimensional maps. Preprint IHES, Bures-sur-Yvette (1979).Google Scholar
  7. N. Metropolis, M.L. Stein, P.R. Stein. On finite limit sets for transformations on the unit interval. J. Comb. Theory (A) 15, 25 (1973).Google Scholar
  8. J. Guckenheimer. On the bifurcation of maps of the interval. Inventiones Math. 39, 165 (1977).Google Scholar
  9. O.E. Lanford III. Private communication.Google Scholar
  10. M. Feigenbaum. Quantitative universality for a class of non-linear transformations. J. Stat. Phys. 19, 25 (1978).Google Scholar
  11. P. Collet, J.-P. Eckmann, O.E. Lanford. Universal properties of maps on an interval, to appear.Google Scholar
  12. P. Collet, J.-P. Eckmann. A renormalization group analysis of the hierarchical model in statistical mechanics. Lecture Notes in Phys. Vol. 74.Google Scholar
  13. V. Franceschini, C. Tebaldi. Sequences of infinite bifurcations and turbulence in a 5-modes truncation of the Navier-Stokes equations. J. Stat. Phys., to appear.Google Scholar
  14. V. Franceschini. A Feigenbaum sequence of bifurcations in the Lorenz model. Preprint. University of Modena (1979).Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • P. Collet
    • 1
  • J. -P. Eckman
    • 2
  1. 1.Harvard UniversityUSA
  2. 2.University of GenevaSwitzerland

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