Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Invariant densities for random maps of the interval

Author: S. Pelikan
Journal: Trans. Amer. Math. Soc. 281 (1984), 813-825
MSC: Primary 58F11; Secondary 28D05, 58F13
MathSciNet review: 722776
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A random map is a discrete time process in which one of a number of functions is selected at random and applied. Here we study random maps of $ [0,1]$ which represent dynamical systems on the square $ [0,1] \times [0,1]$. Sufficient conditions for a random map to have an absolutely continuous invariant measure are given, and the number of ergodic components of a random map is discussed.

References [Enhancements On Off] (What's this?)

  • [AR] L. M. Abramov and V. A. Rohlin, The entropy of a skew product of measure-preserving transformations, Amer. Math. Soc. Transl. (2) 48 (1965), 255-265.
  • [DS] N. Dunford and J. T. Schwartz, Linear operators. I, Pure and Appl. Math., Vol. 7, Interscience, New York, 1958.
  • [K] G. Keller, Stochastic stability in some chaotic dynamical systems, preprint. MR 685377 (84k:58130)
  • [LiY] T.-Y. Li and J. A. Yorke, Ergodic transformations from an interval into itself, Trans. Amer. Math. Soc. 235 (1978), 183-192. MR 0457679 (56:15883)
  • [LY] A. Lasota and J. A. Yorke, On the existence of invariant measures for piecewise monotonic transformations, Trans. Amer. Math. Soc. 186 (1973), 481-488. MR 0335758 (49:538)
  • [T] C. Ionescu-Tulcea and G. Marinescu, Théorie ergodique pour des classes d'opérations noncompletement continues, Ann. of Math. (2) 52 (1950), 140-147. MR 0037469 (12:266g)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 58F11, 28D05, 58F13

Retrieve articles in all journals with MSC: 58F11, 28D05, 58F13

Additional Information

Article copyright: © Copyright 1984 American Mathematical Society

American Mathematical Society