$L^{q}$ -spectra of measures on planar non-conformal attractors. (26th November 2021)

• Record Type: Journal Article
• Authors: FALCONER, KENNETH J.; FRASER, JONATHAN M.; LEE, LAWRENCE D.
• Is Part Of: Ergodic theory and dynamical systems. Volume 41:Number 11(2021)
• Page Start: 3288
• Page End: 3306
• Publication Date: 2021-11-26
• Subjects: Lq-spectrum -- generalized q-dimensions -- non-conformal attractor -- modified singular value function -- self-affine measure; 28A80 -- 37C45 -- 15A18; Ergodic theory -- Periodicals; Differentiable dynamical systems -- Periodicals; 515.42
• DOI: 10.1017/etds.2020.106
• Languages: English
• ISSNs: 0143-3857

Abstract

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.