Multifractal analysis for Birkhoff averages on Lalley-Gatzouras repellers
Henry WJ Reeve
TL;DR
This paper extends multifractal analysis of Birkhoff averages to non-conformal Lalley-Gatzouras repellers, providing a variational principle for Hausdorff dimension with measure-dependent Lyapunov exponents.
Contribution
It introduces a conditional variational principle for Hausdorff dimension on non-conformal repellers, expanding previous results to more general settings.
Findings
Established a variational formula for Hausdorff dimension
Extended multifractal analysis to non-conformal self-affine sets
Connected Lyapunov exponents with measure-dependent dynamics
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.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Chaos control and synchronization · Theoretical and Computational Physics