Hausdorff Dimension for Randomly Perturbed Self Affine Attractors

113 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Dimension theory of iterated function systems (2009, background): “This formula remains true under some weaker conditions [61, 29].”
On equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems (2016, methodology): “The analog of Falconer’s Theorem for the Lyapunov dimension of self-affine measures was established in [25].”
Dimension of invariant measures for affine iterated function systems (2019, background): “In [40], Jordan, Pollicott and Simon proved that the Lyapunov dimension dimLY(m,M) is always an upper bound for the Hausdorff dimension of m ◦ (πa), and moreover when ‖Mj‖ < 1/2 for all j, then for L-a.”
Ledrappier-Young formula and exact dimensionality of self-affine measures (2015, background): “This work was partially supported by the grant 346300 for IMPAN from the Simons Foundation and by the Polish MNiSW 2015-2019 matching fund.”