Invariant measures for piecewise convex transformations of an interval

• Autorzy: Christopher Bose , Véronique Maume-Deschamps , Bernard Schmitt , S. Sujin Shin
• Języki publikacji: EN

Abstrakty

EN

We investigate the existence and ergodic properties of absolutely continuous invariant measures for a class of piecewise monotone and convex self-maps of the unit interval. Our assumption entails a type of average convexity which strictly generalizes the case of individual branches being convex, as investigated by Lasota and Yorke (1982). Along with existence, we identify tractable conditions for the invariant measure to be unique and such that the system has exponential decay of correlations on bounded variation functions and Bernoulli natural extension. In the case when there is more than one invariant density we identify a dominant component over which the above properties also hold. Of particular note in our investigation is the lack of smoothness or uniform expansiveness assumptions on the map or its powers.

Kategorie tematyczne

• 37A25: Ergodicity, mixing, rates of mixing
• 37A05: Measure-preserving transformations
• 37A40: Nonsingular (and infinite-measure preserving) transformations
• 37E05: Maps of the interval (piecewise continuous, continuous, smooth)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2002
• Tom: 152
• Numer: 3
• Strony: 263-297

Daty

wydano

2002

Twórcy

autor

Christopher Bose

• Department of Mathematics and Statistics, University of Victoria, P.O. Box 3045, Victoria, B.C., V8W 3P4, Canada

autor

Véronique Maume-Deschamps

• UMR 5584 du CNRS, Laboratoire de Topologie, Université de Bourgogne, B.P. 400, 21011 Dijon Cedex, France

autor

Bernard Schmitt

• UMR 5584 du CNRS, Laboratoire de Topologie, Université de Bourgogne, B.P. 400, 21011 Dijon Cedex, France

autor

S. Sujin Shin

• Department of Mathematics, Korea Advanced Institute of Science and Technology, 373-1, Guseong-dong, Yuseong-gu, Daejon, 305-701, South Korea

Identyfikatory

DOI

10.4064/sm152-3-5