On the mixing coefficients of piecewise monotonic maps

Israel Journal of Mathematics

Volumn 148, Issue , 2005, Pages 1-10

  Aaronson, Jon ^a   Nakada, Hitoshi ^b  

^a TEL AVIV UNIVERSITY   (Israel)

^b KEIO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 32544435600     PISSN: 00212172     EISSN: 15658511     Source Type: Journal    
DOI: 10.1007/BF02775429     Document Type: Article

References (18)

1. [ADSZ] J. Aaronson, M. Denker, O. Sarig and R. Zweimüller, Aperiodicity of cocycles and conditional local limit theorems, Stochastics and Dynamics 4 (2004), 31-62.
2. [B1] F. Blanchard, β-expansions and symbolic dynamics, Theoretical Computer Science 65 (1989), 131-141.
3. [Br] R. C. Bradley, Basic properties of strong mixing conditions, in Dependence in Probability and Statistics (Oberwolfach, 1985), Progress in Probability and Statistics 11, Birkhäuser Boston, Boston, MA, 1986, pp. 165-192.
4. [Go] M. I. Gordin, Stochastic processes generated by number-theoretic endomorphisms (English), Soviet Mathematics Doklady 9 (1968), 1234-1237
5. (translation from Russian: Doklady Akademii Nauk SSSR 182 (1968), 1004-1006).
6. [H-K] F. Hofbauer and G. Keller, Ergodic properties of invariant measures for piecewise monotonic transformations, Mathematische Zeitschrift 180 (1982), 119-140.
7. [I-K] M. Iosifescu and C. Kraaikamp, Metrical Theory of Continued Fractions (Mathematics and its Applications, 547), Kluwer Academic Publishers, Dordrecht, 2002.
8. [Kh] A. Ya. Khintchine, Continued Fractions, P. Noordhoff, Ltd., Groningen, 1963
9. (translation from Russian: Cepnye drobi, Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow-Leningrad, 1935).
10. [Ku] R. Kuzmin, On a problem of Gauss, Doklady Akademii Nauk SSSR, Seriya A (1928), 375-380
11. (Russian; French translation in: Atti Congresso Internaz. Mat. (Bologna, 1928), Tom VI, Zanichelli, Bologna, 1932, pp. 83-89).
12. [L-Y] A. Lasota and J. Yorke, On the existence of invariant measures for piecewise monotonic transformations, Transactions of the American Mathematical Society 186 (1973), 481-488.
13. [L] P. Levy, Théorie de l'addition des variables aléatoires (French), (Monogr. d. probabilit. calcul d. probabilit. et ses appl. 1), XVII, Gauthier-Villars, Paris, 1937.
14. [N-N] H. Nakada and R. Natsui, Some strong mixing properties of a sequence of random variables arising from α-continued fractions, Stochastics Dynamics 3 (2003), 463-476.
15. [Pa] W. Parry, On the β-expansions of real numbers, Acta Mathematica Academiae Scientiarum Hungaricae 11 (1960), 401-416.
16. [Ry] M. Rychlik, Bounded variation and invariant measures, Studia Mathematica 76 (1983), 69-80.
17. [S] J. Schmeling, Symbolic dynamics for β-shifts and self-normal numbers, Ergodic Theory and Dynamical Systems 17 (1997), 675-694.
18. [Z] R. Zweimüller, Ergodic structure and invariant densities of non-Markovian interval maps with indifferent fixed points, Nonlinearity 11 (1998), 1263-1276.