Invariant measures for piecewise convex transformations of an interval

Christopher Bose, et al. "Invariant measures for piecewise convex transformations of an interval." Studia Mathematica 152.3 (2002): 263-297. <http://eudml.org/doc/284495>.

@article{ChristopherBose2002,
abstract = {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.},
author = {Christopher Bose, Véronique Maume-Deschamps, Bernard Schmitt, S. Sujin Shin},
journal = {Studia Mathematica},
keywords = {existence; ergodic properties; absolutely continuous invariant measures; self-maps of the unit interval},
language = {eng},
number = {3},
pages = {263-297},
title = {Invariant measures for piecewise convex transformations of an interval},
url = {http://eudml.org/doc/284495},
volume = {152},
year = {2002},
}

TY - JOUR
AU - Christopher Bose
AU - Véronique Maume-Deschamps
AU - Bernard Schmitt
AU - S. Sujin Shin
TI - Invariant measures for piecewise convex transformations of an interval
JO - Studia Mathematica
PY - 2002
VL - 152
IS - 3
SP - 263
EP - 297
AB - 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.
LA - eng
KW - existence; ergodic properties; absolutely continuous invariant measures; self-maps of the unit interval
UR - http://eudml.org/doc/284495
ER -