ABSOLUTELY CONTINUOUS INVARIANT MEASURES FOR GENERIC MULTI-DIMENSIONAL PIECEWISE AFFINE EXPANDING MAPS
1999
By a well-known result of Lasota and Yorke, any self-map f of the interval which is
piecewisesmooth and uniformly expanding, i.e. such that inf|f′|>1, admits
absolutely continuousinvariant
probability measures(or a.c.i.m.'s for short). The generalization of this statement to higher dimension remains an
open problem. Currently known results only apply to "sufficiently expanding maps". Here we present a different approach which can deal with almost all
piecewiseexpanding maps. Here, we consider both continuous and discontinuous
piecewiseaffine expanding maps.
Keywords:
-
Correction
-
Source
-
Cite
-
Save
11
References
28
Citations
NaN
KQI