Lq-spectra of measures on planar non-conformal attractors.

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+α 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. [ABSTRACT FROM AUTHOR]