Abstract
For the invariant sets of dynamical systems a new notion of dimension-the so-called dimension with respect to a dynamical system-is introduced. It has some common features with the general topological notion of the dimension, but it also reflects the dynamical properties of the system. In the one-dimensional case it coincides with the Hausdorff dimension. For multi-dimensional hyperbolic sets formulae for the calculation of our dimension are obtained. These results are generalizations of Manning's results obtained by him for the Hausdorff dimension in the two-dimensional case.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 405-420 |
| Number of pages | 16 |
| Journal | Ergodic Theory and Dynamical Systems |
| Volume | 4 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 1984 |
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics