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We compute the Hausdorff dimension of limit sets generated by 3-dimensional self-affine mappings with diagonal matrices of the form A_{ijk}=Diag(a_{ijk}, b_{ij}, c_{i}), where 0<a_{ijk}le b_{ij}le c_i<1. By doing so we show that the variational principle for the dimension holds for this class.
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 $
In this paper, we study the Hausdorff and the box dimensions of closed invariant subsets of the space of pointed trees, equipped with a pseudogroup action. This pseudogroup dynamical system can be regarded as a generalization of a shift space. We sho
We show that the graph of the classical Weierstrass function $sum_{n=0}^infty lambda^n cos (2pi b^n x)$ has Hausdorff dimension $2+loglambda/log b$, for every integer $bge 2$ and every $lambdain (1/b,1)$. Replacing $cos(2pi x)$ by a general non-const
A function which is transcendental and meromorphic in the plane has at least two singular values. On one hand, if a meromorphic function has exactly two singular values, it is known that the Hausdorff dimension of the escaping set can only be either
We prove that the Hausdorff dimension of the set of three-period orbits in classical billiards is at most one. Moreover, if the set of three-period orbits has Hausdorff dimension one, then it has a tangent line at almost every point.