Smooth transformations of intervals

Oscar E. Lanford III

Séminaire Bourbaki (1980-1981)

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

How to cite

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.