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$L^{q}$
-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
$C^{1+\alpha }$
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.
