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Mathematics > Dynamical Systems

arXiv:1503.00892 (math)
[Submitted on 3 Mar 2015 (v1), last revised 2 Jun 2015 (this version, v2)]

Title:On the Ledrappier-Young formula for self-affine measures

Authors:Balázs Bárány
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Abstract:Ledrappier and Young introduced a relation between entropy, Lyapunov exponents and dimension for invariant measures of diffeomorphisms on compact manifolds. In this paper, we show that a self-affine measure on the plane satisfies the Ledrappier-Young formula if the corresponding iterated function system (IFS) satisfies the strong separation condition and the linear parts satisfy the dominated splitting condition. We give sufficient conditions, inspired by Ledrappier and by Falconer and Kempton, that the dimensions of such a self-affine measure is equal to the Lyapunov dimension. We show some applications, namely, we give another proof for Hueter-Lalley's theorem and we consider self-affine measures and sets generated by lower triangular matrices.
Subjects: Dynamical Systems (math.DS)
MSC classes: 37C45, 28A80
Cite as: arXiv:1503.00892 [math.DS]
  (or arXiv:1503.00892v2 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.1503.00892
Journal reference: Math. Proc. Camb. Phil. Soc. 159 no. 03 2015, 405 - 432
Related DOI: https://doi.org/10.1017/S0305004115000419

Submission history

From: Balázs Bárány Dr. [view email]
[v1] Tue, 3 Mar 2015 10:52:03 UTC (261 KB)
[v2] Tue, 2 Jun 2015 10:21:52 UTC (315 KB)
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