On natural invariant measures on generalised iterated function systems

By A. Käenmäki. 2017

104 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/4bfdf823c61b0549bbdb614578baf1314466d338

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In Mathematical Physics

Citations in the corpus

Dimension theory of iterated function systems (2009, unknown): “Käenmäki [30] proved that for “almost all” self-affine sets there exists an ergodic measure m so that m ◦ π−1 is of full Hausdorff dimension.”
Equilibrium states for factor maps between subshifts (2011, background): “It was also obtained in [18] for the case that φ > 0.”
Non-conformal Repellers and the Continuity of Pressure for Matrix Cocycles (2013, result): “The existence of ergodic equilibrium measures was proved by Käenmäki [28] under fairly general conditions (but more restrictive than the above theorem).”
Equilibrium states of the pressure function for products of matrices (2010, background): “3) was proved earlier in [7, 15] when the matrices are non-negative or invertible, respectively.”
Dimension of invariant measures for affine iterated function systems (2019, background): “This was first proved by Käenmäki [41] in the case when S is invertible, and it extends to the general case by the sub-additive thermodynamic formalism [16].”
Hausdorff Dimension for Randomly Perturbed Self Affine Attractors (2007, methodology): “The measure µ in Proposition 1 is the same as that constructed by Käenmäki in [8].”
Hausdorff dimension of planar self-affine sets and measures (2017, methodology): “In order to show this approximation property, Morris and Shmerkin used the Käenmäki measure, which is in our setup the unique ergodic shift invariant measure, for which dimL μ = dimAX, see [24, 25].”
On equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems (2016, background): “We restrict ourselves to the planar case, and refer to [27] for details and proofs.”
The thermodynamic formalism for sub-additive potentials (2007, background): “We were also informed that Käenmäki [17] proved the variational principle on full shift symbolic spaces for a class of special sub-additive potentials F = {log fn} (where fn(x) were assumed to depend upon only the first n coordinates of x) using the upper semi-continuity of the entropy map on symb”
Lyapunov Spectrum of Asymptotically Sub-additive Potentials (2009, background): “We remark that the variational principle for sub-additive potentials has been studied in [18, 3, 25, 31, 35, 4, 40] under additional assumptions on the corresponding sub-additive potential and TDS.”