Let M be a smooth compact manifold of any dimension. We consider the set of C1 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 C1 topology.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics