Lq-spectra of measures on planar non-conformal attractors
Abstract
We study the Lq-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 C1+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 Lq-spectrum of Bernoulli measures supported on such sets by using an appropriately defined analogue of the singular value function and an appropriate pressure function.
Citation
Falconer , K J , Fraser , J & Lee , L D 2021 , ' L q -spectra of measures on planar non-conformal attractors ' , Ergodic Theory and Dynamical Systems , vol. 41 , no. 11 , pp. 3288-3306 . https://doi.org/10.1017/etds.2020.106
Publication
Ergodic Theory and Dynamical Systems
Status
Peer reviewed
ISSN
0143-3857Type
Journal article
Description
Funding: KJF and JMF were supported by an EPSRC Standard Grant (EP/R015104/1). JMF was also supported by a Leverhulme Trust Research Project Grant (RPG-2019-034). LDL was supported by an EPSRC Doctoral Training Grant.Collections
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