منابع مشابه
Assouad Dimension of Self-affine Carpets
We calculate the Assouad dimension of the self-affine carpets of Bedford and McMullen, and of Lalley and Gatzouras. We also calculate the conformal Assouad dimension of those carpets that are not self-similar.
متن کاملThe Hausdorff Dimension of the Projections of Self-affine Carpets
We study the orthogonal projections of a large class of self-affine carpets, which contains the carpets of Bedford and McMullen as special cases. Our main result is that if Λ is such a carpet, and certain natural irrationality conditions hold, then every orthogonal projection of Λ in a non-principal direction has Hausdorff dimension min(γ, 1), where γ is the Hausdorff dimension of Λ. This gener...
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Affine processes are distinguished by their rich structural properties, which makes them favorite when it comes to computations in financial applications of all kind. This fact has been explored and illustrated for the time-homogeneous case in a recent paper by Duffie, Filipović and Schachermayer. However, there are many situations which require time-dependent parameters, such as when it comes ...
متن کاملGibbs measures on self-affine Sierpinski carpets and their singularity spectrum
We consider a class of Gibbs measures on self-affine Sierpinski carpets and perform the multifractal analysis of its elements. These deterministic measures are Gibbs measures associated with bundle random dynamical systems defined on probability spaces whose geometrical structure plays a central rôle. A special subclass of these measures is the class of multinomial measures on Sierpinski carpet...
متن کاملSelf-similar carpets over finite fields
In [4] an informal algorithm ’to display interesting numeric patterns’ is described without any proof. We generalize this algorithm over arbitrary finite fields of characteristic p and we prove that it really generates self-similar carperts, provided that they contain at least one zero in the first (p+1)/2 lines. For the fields Fp the generalized algorithm produces p− 1 different self-similar c...
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ژورنال
عنوان ژورنال: Indiana University Mathematics Journal
سال: 2016
ISSN: 0022-2518
DOI: 10.1512/iumj.2016.65.5903