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arXiv · 2005.09361

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

Kenneth J. Falconer·Jonathan M. Fraser·Lawrence D. Lee
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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 $C^{1+\alpha}$ 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.

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BibTeXRIS

Kenneth J. Falconer, Jonathan M. Fraser, Lawrence D. Lee. 2020-05-19. $L^q$-spectra of measures on planar non-conformal attractors. https://arxiv.org/abs/2005.09361

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