Abstract
We obtain bounds for the generalized q-dimensions of measures supported by self-affine sets that ate valid for 'almost all' families of affine mappings. Exact values are established for self-affine measures and for Gibbs measures when 1 < q less than or equal to 2. These q-dimensions may exhibit phase transitions as q varies.
Original language | English |
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Pages (from-to) | 877-891 |
Number of pages | 15 |
Journal | Nonlinearity |
Volume | 12 |
Issue number | 4 |
DOIs | |
Publication status | Published - Jul 1999 |
Keywords
- STRANGE ATTRACTORS
- MULTIFRACTAL FORMALISM
- HAUSDORFF DIMENSION
- SIERPINSKI CARPETS
- FRACTALS
- SPECTRUM