L^q -spectra of measures on planar non-conformal attractors. (26th November 2021) - FALCONER, KENNETH J.; FRASER, JONATHAN M.; LEE, LAWRENCE D.
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+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.