Balázs Bárány
Published 2015-03-03Version 1
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 so called dominated splitting. We give a sufficient condition, inspired by Ledrappier, 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 classical theorem and we consider self-affine measures and sets generated by lower triangular matrices.
On self-affine measures associated to strongly irreducible and proximal systems
On self-affine measures with equal Hausdorff and Lyapunov dimensions
Ledrappier-Young formulae for a family of nonlinear attractors
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