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Multifractal analysis for Birkhoff averages on Lalley–Gatzouras repellers

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Author(s): Henry W. J. Reeve
Source:
Fundamenta Mathematicae. 212:71-93
Subject Terms:
Class (set theory); Pure mathematics; Mathematics::Dynamical Systems; Algebra and Number Theory; Mathematical analysis; Multifractal system; Lyapunov exponent; Measure (mathematics); Set (abstract data type); symbols.namesake; Variational principle; Hausdorff dimension; symbols; Limit (mathematics); Mathematics
Online Access:
https://explore.openaire.eu/search/publication?articleId=doi_________::e1bf0242a72167f51aa25d409554d92b
https://doi.org/10.4064/fm212-1-5

Additional Information
- Publication Information:
  Institute of Mathematics, Polish Academy of Sciences, 2011.
- Publication Date:
  2011
- Abstract:
  We consider the multifractal analysis for Birkhoff averages of continuous potentials on a class of non-conformal repellers corresponding to the self-affine limit sets studied by Lalley and Gatzouras. A conditional variational principle is given for the Hausdorff dimension of the set of points for which the Birkhoff averages converge to a given value. This extends a result of Barral and Mensi to certain non-conformal maps with a measure dependent Lyapunov exponent.
- ISSN:
  1730-6329
  0016-2736
- Rights:
  OPEN
- Accession Number:
  edsair.doi...........e1bf0242a72167f51aa25d409554d92b

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