Invariant measures for piecewise convex transformations of an interval

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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.
Publisher
POLISH ACAD SCIENCES INST MATHEMATICS
Issue Date
2002
Language
English
Article Type
Article
Citation

STUDIA MATHEMATICA, v.152, no.3, pp.263 - 297

ISSN
0039-3223
URI
http://hdl.handle.net/10203/83177
Appears in Collection
MA-Journal Papers(저널논문)
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