Abstract
Sufficient conditions are given such that a differentiable, non invertible, mapg:[0, 1]↦[0, 1] leaves invariant a measure absolutely continuous with respect to the Lebesgue measure. In particular, this is shown to be the case forg(x)=Rx(1−x) whenR=3,6785735 ... .
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Bibliographie
Dunet, H., Sakowitsch, M., Taranco, A.: Etude de mesures invariantes par une famille de transformations liées à la biologie. Thèse 3ème cycle, Paris VII (1975)
Iakobson, M.V.: On smooth mappings of the circle into itself. Mat. Sbornik85, 163–188 (1971)
Lasota, A., Yorke, J.A.: On the existence of invariant measures for piecewise monotonic transformations. Trans. Amer. Math. Soc.186, 481–488 (1973)
Lorenz, E.N.: Deterministic nonperiodic flow. J. atmos. Sci.20, 130–141 (1963)
May, R.M.: Simple mathematical models with very complicated dynamics. Nature261, 459–467 (1976)
Ruelle, D.: Thermodynamic formalism. Reading, Mass.: Addison-Wesley (to appear)
Ruelle, D., Takens, F.: On the nature of turbulence. Commun. math. Phys.20, 167–192 (1971);23, 343–344 (1971)
Ulam, S.M., Neumann, J. von: On combination of stochastic and deterministic processes. Preliminary report. Bull. Amer. Math. Soc.53, 1120 (1947)
Author information
Authors and Affiliations
Additional information
Transmis par J. L. Lebowitz
Rights and permissions
About this article
Cite this article
Ruelle, D. Applications conservant une mesure absolument continue par rapport àdx sur [0, 1]. Commun.Math. Phys. 55, 47–51 (1977). https://doi.org/10.1007/BF01613148
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01613148