A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2008; you can also visit the original URL.
The file type is `application/pdf`

.

##
###
A generic C1 map has no absolutely continuous invariant probability measure

2006
*
Nonlinearity
*

Let M be a smooth compact manifold of any dimension. We consider the set of C 1 maps f : M → M which have no absolutely continuous (with respect to Lebesgue) invariant probability measure. We show that this is a residual set in the C 1 topology. Mathematics Subject Classification: 37C40 Statement Let M be a smooth compact manifold (maybe with boundary, maybe disconnected) of any dimension d 1. Let m be some (smooth) volume probability measure in M. Let C 1 (M, M) be the set of C 1 maps M → M,

doi:10.1088/0951-7715/19/11/011
fatcat:vjqumyddpreijetpcrz4mjgh3e