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$L^{q}$-spectra of measures on planar non-conformal attractors

Published online by Cambridge University Press:  26 October 2020

School of Mathematics & Statistics, University of St Andrews, St Andrews, KY16 9SS, UK (e-mail:,
School of Mathematics & Statistics, University of St Andrews, St Andrews, KY16 9SS, UK (e-mail:,
School of Mathematics & Statistics, University of St Andrews, St Andrews, KY16 9SS, UK (e-mail:,


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.

Original Article
© The Author(s), 2020. Published by Cambridge University Press

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