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

2020/05/19 by K. J. Falconer, Falconer, Kenneth J., Jonathan M. Fraser +3 · 3 citations
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Advanced Differential Equations and Dynamical Systems

paper · pdf · doi:10.48550/arxiv.2005.09361

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.

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• Generalized q-dimensions of measures on Non-autonomous conformal sets
• Dimension estimates for C¹ iterated function systems and repellers. Part II
• Multifractal Analysis of Equilibrium States of Endomorphisms of ℙ^k

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