1 results
$L^{q}$
-spectra of measures on planar non-conformal attractors
- Part of
-
- Journal:
- Ergodic Theory and Dynamical Systems / Volume 41 / Issue 11 / November 2021
- Published online by Cambridge University Press:
- 26 October 2020, pp. 3288-3306
- Print publication:
- November 2021
-
- Article
- Export citation
-
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.
