Some limit ratio theorem related to a real endomorphism in case of a neutral fixed point
Collet, P. ; Ferrero, P.
Annales de l'I.H.P. Physique théorique, Tome 52 (1990), p. 283-301 / Harvested from Numdam
@article{AIHPA_1990__52_3_283_0,
     author = {Collet, P. and Ferrero, Pierre},
     title = {Some limit ratio theorem related to a real endomorphism in case of a neutral fixed point},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {52},
     year = {1990},
     pages = {283-301},
     mrnumber = {1057449},
     zbl = {0703.58016},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1990__52_3_283_0}
}
Collet, P.; Ferrero, P. Some limit ratio theorem related to a real endomorphism in case of a neutral fixed point. Annales de l'I.H.P. Physique théorique, Tome 52 (1990) pp. 283-301. http://gdmltest.u-ga.fr/item/AIHPA_1990__52_3_283_0/

[A] J. Aaronson, The asymptotic distributional behaviour of transformations preserving infinite measures, J. Anal. Math., Vol. 39, 1981, p. 203. | MR 632462 | Zbl 0499.28013

[B] R. Bowen, Invariant measures for Markov maps of the interval, Comm. Math. Phys., Vol. 69, 1979, p. 1. | MR 547523 | Zbl 0421.28016

[BU] P. Bugiel, A note on invariant measures for Markov maps of an interval, Z. Wahr. U. Gebiete, Vol. 70, 1985, p. 345. | MR 803676 | Zbl 0606.28013

[C-F] P. Collet and P. Ferrero, Absolutely continuous invariant measure for expanding Pick maps of the interval except at a marginal fixed point, in Instabilities and Nonequilibrium Structures, E. TIRAPEGUI and D. VILLAROEL Eds., Kluwer Academic Publishers, 1989. | MR 1032559 | Zbl 0706.58030

[D] N.G. De Bruyn, Asymptotic methods in analysis, North Holland, Amsterdam, London, 1958. | MR 99564

[F] M. Feigenbaum, Complicated objects on regular trees, in Nonlinear Evolutions and Chaotic Phenomena, G. GALLAVOTTI and P. ZWEIFEL, Eds., Nato asi series, Vol. 176, Plenum press, New York, 1988. | MR 1109967 | Zbl 0708.58008

[G-W] P. Gaspard and X.J. Wang, Sporadicity: Between periodic and chaotic dynamical behaviors, Proc. Nat. Acad. Sci., Vol. 85, 1988, p. 4591. | MR 949187 | Zbl 0668.58029

[H] G.H. Hardy, Divergent series, Oxford University Press, Oxford, 1973. | MR 30620

[K] U. Krengel, Ergodic Theorems, De Gruyter Studies in Mathematics, Vol. 6, Walter de Gruyter, Berlin, New York, 1985. | MR 797411 | Zbl 0575.28009

[L-Y] A. Lasota, J. Yorke, On the existence of invariant measures for piecewise monotonic transformations, Trans. Am. Math. Soc., Vol. 186, 1973, p. 481. | MR 335758 | Zbl 0298.28015

[M] B.B. Mandelbrot, Fractals, Form, Chance, and Dimension, Freeman and Co., New York, 1977. | MR 471493

[Ma] P. Manneville, Intermittency, self-similarity and 1/f spectrum in dissipative dynamical systems, J. Phys. France, Vol. 41, 1980, p. 1235. | MR 592697

[Me] C. Meunier, Continuity of type 1 intermittency from a measure theorical point of view, J. Stat. Phys., Vol. 36, 1984, p. 321. | MR 780673 | Zbl 0588.58052

[N] J. Neveu, Bases Mathématiques du Calcul des Probabilités, Masson, Paris, 1970. | MR 272004 | Zbl 0203.49901

[T] M. Thaler, Estimates of the invariant densities of endomorphisms with indifferent fixed points, Isr. J. Math., Vol. 37, 1980, p. 303. | MR 599464 | Zbl 0447.28016

[Ti] E.C. Titchmarsh, The Theory of Functions, Oxford University Press, Oxford, 1932. | Zbl 0005.21004