Geodesic
Most expanding maps have no absolutely continuous invariant measure
Studia Mathematica, Tome 134 (1999) no. 1, pp. 69-78

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

DOI

We consider the topological category of various subsets of the set of expanding maps from a manifold to itself, and show in particular that a generic $C^1$ expanding map of the circle has no absolutely continuous invariant probability measure. This is in contrast with the situation for $C^2$ or $C^{1+ε}$ expanding maps, for which it is known that there is always a unique absolutely continuous invariant probability measure.
DOI : 10.4064/sm-134-1-69-78
Keywords: $C^1$ expanding map, Ruelle-Perron-Frobenius operator 
Anthony N. Quas. Most expanding maps have no absolutely continuous invariant measure. Studia Mathematica, Tome 134 (1999) no. 1, pp. 69-78. doi: 10.4064/sm-134-1-69-78
@article{10_4064_sm_134_1_69_78,
     author = {Anthony N. Quas},
     title = {Most expanding maps have no absolutely continuous invariant measure},
     journal = {Studia Mathematica},
     pages = {69--78},
     year = {1999},
     volume = {134},
     number = {1},
     doi = {10.4064/sm-134-1-69-78},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-134-1-69-78/}
}
TY  - JOUR
AU  - Anthony N. Quas
TI  - Most expanding maps have no absolutely continuous invariant measure
JO  - Studia Mathematica
PY  - 1999
SP  - 69
EP  - 78
VL  - 134
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm-134-1-69-78/
DO  - 10.4064/sm-134-1-69-78
LA  - en
ID  - 10_4064_sm_134_1_69_78
ER  - 
%0 Journal Article
%A Anthony N. Quas
%T Most expanding maps have no absolutely continuous invariant measure
%J Studia Mathematica
%D 1999
%P 69-78
%V 134
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/sm-134-1-69-78/
%R 10.4064/sm-134-1-69-78
%G en
%F 10_4064_sm_134_1_69_78

Cité par Sources :