Generalized dimensions of measures on self-affine sets

Authors
Falconer, KJ
Citation
Kj. Falconer, Generalized dimensions of measures on self-affine sets, NONLINEARIT, 12(4), 1999, pp. 877-891
Citations number
30
Categorie Soggetti
Mathematics
Journal title
NONLINEARITY
ISSN journal
09517715 → ACNP
Volume
12
Issue
4
Year of publication
1999
Pages
877 - 891
Database
ISI
SICI code
0951-7715(199907)12:4<877:GDOMOS>2.0.ZU;2-I
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 mapping s. Exact values are established for self-affine measures and for Gibbs meas ures when 1 < q less than or equal to 2. These q-dimensions may exhibit pha se transitions as q varies.