Summary
It is shown that the transformation x↦gbx+α (mod 1) (β>1, 0≦α<1) on [0, 1] has unique maximal measure.
Article PDF
Similar content being viewed by others
References
Hofbauer, F.: β-shifts have unique maximal measures. Monatsh. Math. 85, 189–198 (1978)
Hofbauer, F.: On intrinsic ergodicity of piecewise monotonic transformations with positive entropy I, II. Israel J. Math. 34, 213–237 (1979)
Denker, M., Grillenberger, Ch., Sigmund, K.: Ergodic theory on compact spaces. Lectures notes in Mathematics 527. Berlin-Heidelberg-New York: Springer 1976
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hofbauer, F. Maximal measures for simple piecewise monotonic transformations. Z. Wahrscheinlichkeitstheorie verw Gebiete 52, 289–300 (1980). https://doi.org/10.1007/BF00538893
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00538893