Hausdorff dimension estimates for non-injective maps using the cardinality of the pre-image sets
Astrid Franz; Astrid Franz; Institute of Physics, Theoretical Physics, Computational Physics, University of Technology Chemnitz, 09107 Chemnitz, Germany
Журнал:
Nonlinearity
Дата:
2000-09-01
Аннотация:
Upper bounds for the Hausdorff dimension of compact invariant sets of C<sup>1</sup>-maps on smooth Riemannian manifolds are given in terms of the singular values of the tangent map and the multiplicity function of the map, describing the number of pre-images of a certain point in a given set. For non-injective maps this improves previous results using only the singular values.
142.5Кб