Physical measures for infinite-modal maps

Vítor Araújo, and Maria José Pacifico. "Physical measures for infinite-modal maps." Fundamenta Mathematicae 203.3 (2009): 211-262. <http://eudml.org/doc/282984>.

@article{VítorAraújo2009,
abstract = {We analyze certain parametrized families of one-dimensional maps with infinitely many critical points from the measure-theoretical point of view. We prove that such families have absolutely continuous invariant probability measures for a positive Lebesgue measure subset of parameters. Moreover, we show that both the density of such a measure and its entropy vary continuously with the parameter. In addition, we obtain exponential rate of mixing for these measures and also show that they satisfy the Central Limit Theorem.},
author = {Vítor Araújo, Maria José Pacifico},
journal = {Fundamenta Mathematicae},
keywords = {SRB measures; absolutely continuous invariant measures; infinite-modal maps; statistical stability; exponential decay of correlations; central limit theorem; continuous variation of entropy},
language = {eng},
number = {3},
pages = {211-262},
title = {Physical measures for infinite-modal maps},
url = {http://eudml.org/doc/282984},
volume = {203},
year = {2009},
}

TY - JOUR
AU - Vítor Araújo
AU - Maria José Pacifico
TI - Physical measures for infinite-modal maps
JO - Fundamenta Mathematicae
PY - 2009
VL - 203
IS - 3
SP - 211
EP - 262
AB - We analyze certain parametrized families of one-dimensional maps with infinitely many critical points from the measure-theoretical point of view. We prove that such families have absolutely continuous invariant probability measures for a positive Lebesgue measure subset of parameters. Moreover, we show that both the density of such a measure and its entropy vary continuously with the parameter. In addition, we obtain exponential rate of mixing for these measures and also show that they satisfy the Central Limit Theorem.
LA - eng
KW - SRB measures; absolutely continuous invariant measures; infinite-modal maps; statistical stability; exponential decay of correlations; central limit theorem; continuous variation of entropy
UR - http://eudml.org/doc/282984
ER -