Lq-spectra of measures on planar non-conformal attractors

Kenneth John Falconer, Jonathan Fraser, Lawrence David Lee*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
22 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)3288-3306
Number of pages19
JournalErgodic Theory and Dynamical Systems
Issue number11
Early online date26 Oct 2020
Publication statusPublished - Nov 2021


  • Lq-spectrum
  • Generalised q-dimensions
  • Non-conformal attractor
  • Modified singular value function
  • Self-affine measure


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