Are the dimensions of a set and its image equal under typical smooth functions ?

@inproceedings{Sauer2014AreTD,
  title={Are the dimensions of a set and its image equal under typical smooth functions ?},
  author={Timothy D. Sauer and J. A. Yorke},
  year={2014}
}
We examine the question whether the dimension D of a set or probability measure is the same as the dimension of its image under a typical smooth function, if the range space is at least D-dimensional. If is a Borel probability measure of bounded support in Rn with correlation dimension D, and if m D, then under almost every continuously differentiable function (“almost every” in the sense of prevalence) from Rn to Rm, the correlation dimension of the image of is also D. If is the invariant… CONTINUE READING