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Hausdorff and Fractal Dimension Estimates for Invariant Sets of Non-Injective Maps
| Content Provider | Semantic Scholar |
|---|---|
| Author | Boichenko, Vladimir A. Franz, Achim Leonov, Gennady A. Reitmann, Volker |
| Copyright Year | 1998 |
| Abstract | In this paper we are concerned with upper bounds for the Hausdorif and fractal dimensions of negatively invariant sets of maps on Riemannian manifolds. We consider a special class of non-injective maps, for which we introduce a factor describing the "degree of non-injectivity". This factor can be included in the Hausdorif dimension estimates of DouadyOesterlé type [2, 7, 10] and in fractal dimension estimates [5, 13, 15] in order to weaken the condition to the singular values of the tangent map. In a number of cases we get better upper dimension estimates. |
| Starting Page | 207 |
| Ending Page | 223 |
| Page Count | 17 |
| File Format | PDF HTM / HTML |
| DOI | 10.4171/ZAA/816 |
| Volume Number | 17 |
| Alternate Webpage(s) | https://www.ems-ph.org/journals/show_pdf.php?iss=1&issn=0232-2064&rank=13&vol=17 |
| Alternate Webpage(s) | https://doi.org/10.4171/ZAA%2F816 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
