Weak separation condition, Assouad dimension, and Furstenberg homogeneity
نویسندگان
چکیده
منابع مشابه
Equi-homogeneity, Assouad Dimension and Non-autonomous Dynamics
A fractal, as originally described by Mandelbrot, is a set with an irregular and fragmented shape. Many fractals that have been extensively studied, such as self-similar sets, have the same degree of irregularity and fragmentation at all length scales. In contrast to this, an equi-homogeneous set is an irregular and fragmented shape that at each fixed scale is identical at every point. We show ...
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Let α ≥ 1 and let (X, d, μ) be an α-homogeneous metric measure space with conformal Assouad dimension equal to α. Then there exists a weak tangent of (X, d, μ) with uniformly big 1-modulus.
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We define a new separation property on the family of contractive similitudes that allows certain overlappings. This property is weaker than the open set condition of Hutchinson. It includes the well-known class of infinite Bernoulli convolutions associated with the P.V. numbers and the solutions of the two-scale dilation equations. Our main purpose in this paper is to prove the multifractal for...
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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 کاملOn the Assouad dimension of self-similar sets with overlaps
It is known that, unlike the Hausdorff dimension, the Assouad dimension of a self-similar set can exceed the similarity dimension if there are overlaps in the construction. Our main result is the following precise dichotomy for self-similar sets in the line: either the weak separation property is satisfied, in which case the Hausdorff and Assouad dimensions coincide; or the weak separation prop...
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ژورنال
عنوان ژورنال: Annales Academiae Scientiarum Fennicae Mathematica
سال: 2016
ISSN: 1239-629X,1798-2383
DOI: 10.5186/aasfm.2016.4133