Article contents
$L^{q}$-spectra of measures on planar non-conformal attractors
Published online by Cambridge University Press: 26 October 2020
Abstract
We study the $L^{q}$ -spectrum of measures in the plane generated by certain nonlinear maps. In particular, we consider attractors of iterated function systems consisting of maps whose components are $C^{1+\alpha }$ and for which the Jacobian is a lower triangular matrix at every point subject to a natural domination condition on the entries. We calculate the $L^{q}$ -spectrum of Bernoulli measures supported on such sets by using an appropriately defined analogue of the singular value function and an appropriate pressure function.
Keywords
MSC classification
- Type
- Original Article
- Information
- Copyright
- © The Author(s), 2020. Published by Cambridge University Press
References
- 4
- Cited by