Smooth transformations of intervals

Oscar E. Lanford III

Séminaire Bourbaki (1980-1981)

  • Volume: 23, page 36-54
  • ISSN: 0303-1179

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Lanford III, Oscar E.. "Smooth transformations of intervals." Séminaire Bourbaki 23 (1980-1981): 36-54. <http://eudml.org/doc/109979>.

@article{LanfordIII1980-1981,
author = {Lanford III, Oscar E.},
journal = {Séminaire Bourbaki},
keywords = {unimodal mapping; periodic orbit; everywhere continuously differentiable mappings; negative Schwarzian condition; period doubling bifurcation; universal sequence of periodic regimes; doubling operator; Feigenbaum theory},
language = {eng},
pages = {36-54},
publisher = {Springer-Verlag},
title = {Smooth transformations of intervals},
url = {http://eudml.org/doc/109979},
volume = {23},
year = {1980-1981},
}

TY - JOUR
AU - Lanford III, Oscar E.
TI - Smooth transformations of intervals
JO - Séminaire Bourbaki
PY - 1980-1981
PB - Springer-Verlag
VL - 23
SP - 36
EP - 54
LA - eng
KW - unimodal mapping; periodic orbit; everywhere continuously differentiable mappings; negative Schwarzian condition; period doubling bifurcation; universal sequence of periodic regimes; doubling operator; Feigenbaum theory
UR - http://eudml.org/doc/109979
ER -

References

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  1. [1] M. Campanino, H. Epstein, and D. Ruelle, "On Feigenbaum's tunctional 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). Zbl0474.58013
  2. [2] P. Collet and J.-P. Eckmann, "Iterated Maps on the Interval as Dynamical Systems", Birkhäuser, Boston-Basel-Stuttgart, 1980. Zbl0458.58002MR613981
  3. [3] P. Collet, J.-P. Eckmann, and O.E. Lanford, "Universal properties of maps on an interval", Commun. Math. Phys.76 (1980) 211-254. Zbl0455.58024MR588048
  4. [4] M. Feigenbaum, "Quantitative universality for a class of non-linear transformations", J. Stat. Phys.19 (1978) 25-52. Zbl0509.58037MR501179
  5. "The universal metric properties of non-linear transformation", J. Stat. Phys.21 (1979) 669-706. Zbl0515.58028MR555919
  6. [5] J. Guckenheimer, "Bifurcations of maps of the interval", Inventiones Math.39 (1977) 165-178. Zbl0354.58013MR438399
  7. [6] J. Guckenheimer, "Sensitive dependence on initial conditions for one dimensional maps", Commun. Math. Phys.70 (1979) 133-160. Zbl0429.58012MR553966
  8. [7] E.N. Lorenz, "On the prevalence of aperiodicity for simple systems", Springer Lecture Notes in Mathematics755 (1979) 53-77. Zbl0438.34038MR564902
  9. [8] R.B. May, "Simple mathematical models with very complicated dynamics", Nature261 (1976) 459-467. 
  10. [9] M. Metropolis, M.L. Stein, and P.R. Stein, "On finite limit sets for transformations of the unit interval", J. Combinatorial Theory15 (1973) 25-44. Zbl0259.26003MR316636
  11. [10] M. Misiurewicz, "Absolutely continuous measures for certain maps of an interval", IHES preprint, M/79/293(1979). MR623533
  12. [11] D. Singer, "Stable orbits and bifurcations of maps of the interval", SIAM J. Appl. Math.35(1978) 260-267. Zbl0391.58014MR494306
  13. [12] P. Coullet and J. Tresser, "Itérations d'endomorphismes et groupe de renormalisation", C.R. Acad. Sci., Paris287(1978) 577-580. Zbl0402.54046
  14. "Itérations d'endomorphismes et groupe de renormalisation", Journal de Physique39(1978) C5-25-C5-28. Zbl0402.54046

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