Lq-spectra of measures on planar non-conformal attractors

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

DOI

https://doi.org/10.1017/etds.2020.106

ISSN

0143-3857

Type

Journal article

Rights

Copyright © The Author(s), 2020. Published by Cambridge University Press. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1017/etds.2020.106.

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.