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We prove that the upper box dimension of an inhomogeneous self-affine set is bounded above by the maximum of the affinity dimension and the dimension of the condensation set. In addition, we determine sufficient conditions for this upper bound to be attained, which, in part, constitutes an exploration of the capacity for the condensation set to mitigate dimension drop between the affinity dimension and the corresponding homogeneous attractor. Our work improves and unifies previous results on general inhomogeneous attractors, low-dimensional affine systems, and inhomogeneous self-affine carpets, while providing inhomogeneous analogues of Falconers seminal results on homogeneous self-affine sets.
We study equilibrium measures (Kaenmaki measures) supported on self-affine sets generated by a finite collection of diagonal and anti-diagonal matrices acting on the plane and satisfying the strong separation property. Our main result is that such me
Given a non-empty bounded subset of hyperbolic space and a Kleinian group acting on that space, the orbital set is the orbit of the given set under the action of the group. We may view orbital sets as bounded (often fractal) subsets of Euclidean spac
In this paper we compute the dimension of a class of dynamically defined non-conformal sets. Let $Xsubseteqmathbb{T}^2$ denote a Bedford-McMullen set and $T:Xto X$ the natural expanding toral endomorphism which leaves $X$ invariant. For an open set $
Let $E$ be a Bedford-McMullen carpet associated with a set of affine mappings ${f_{ij}}_{(i,j)in G}$ and let $mu$ be the self-affine measure associated with ${f_{ij}}_{(i,j)in G}$ and a probability vector $(p_{ij})_{(i,j)in G}$. We study the asymptot
Twenty five years ago U. Pinkall discovered that the Korteweg-de Vries equation can be realized as an evolution of curves in centoraffine geometry. Since then, a number of authors interpreted various properties of KdV and its generalizations in terms