Results 1 to 10 of about 3,294 (223)
Lowness for effective Hausdorff dimension [PDF]
Journal of Mathematical Logic, 2014 We examine the sequences A that are low for dimension, i.e. those for which the effective (Hausdorff) dimension relative to A is the same as the unrelativized effective dimension. Lowness for dimension is a weakening of lowness for randomness, a central notion in effective randomness.
Steffen Lempp +4 more
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Rigidity, Graphs and Hausdorff Dimension [PDF]
, 2021 For a compact set $E \subset \mathbb R^d$ and a connected graph $G$ on $k+1$ vertices, we define a $G$-framework to be a collection of $k+1$ points in $E$ such that the distance between a pair of points is specified if the corresponding vertices of $G$ are connected by an edge.
Chatzikonstantinou, N. +3 more
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On the Hausdorff dimension of the mather quotient [PDF]
Communications on Pure and Applied Mathematics, 2008 AbstractUnder appropriate assumptions on the dimension of the ambient manifold and the regularity of the Hamiltonian, we show that the Mather quotient is small in term of the Hausdorff dimension. Then we present applications in dynamics. © 2008 Wiley Periodicals, Inc.
Fathi, Albert +2 more
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On Simon’s Hausdorff Dimension Conjecture [PDF]
, 2021 Barry Simon conjectured in 2005 that the Szegő matrices, associated with Verblunsky coefficients $\{α_n\}_{n\in\mathbb{Z}_+}$ obeying $\sum_{n = 0}^\infty n^γ|α_n|^2 < \infty$ for some $γ\in (0,1)$, are bounded for values $z \in \partial \mathbb{D}$ outside a set of Hausdorff dimension no more than $1 - γ$.
Damanik, David +3 more
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International Journal of Mathematics and Mathematical Sciences, 1995 We define the coordinate d-dimension print to distinguish sets of same fractal dimension, and investigate its geometrical properties.
Hung Hwan Lee, In Soo Baek
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Hausdorff–Lebesgue Dimension of Attractors [PDF]
International Journal of Bifurcation and Chaos, 2017 Definitions of Hausdorff–Lebesgue measure and dimension are introduced. Combination of Hausdorff and Lebesgue ideas are used. Methods for upper and lower estimations of attractor dimensions are developed.
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Analysis and Geometry in Metric Spaces, 2020 This paper studies the Hausdorff dimension of the intersection of isotropic projections of subsets of ℝ2n, as well as dimension of intersections of sets with isotropic planes. It is shown that if A and B are Borel subsets of ℝ2n of dimension greater than
Román-García Fernando
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Some typical properties of dimensions of sets and measures
Abstract and Applied Analysis, 2005 This paper contains a review of recent results concerning typical properties of dimensions of sets and dimensions of measures. In particular, we are interested in the Hausdorff dimension, box dimension, and packing dimension of sets and in the Hausdorff ...
Józef Myjak
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Physically based method for determining the Hausdorff’s topological dimension of capillary-porous media [PDF]
BIO Web of ConferencesThe soil structure the solid phase and pore space of the soils are a set of self-similar parts of each other at different levels ( for example, on level aggregates, micro-aggregates or elementary particles of soil).
Moiseev Kirill +3 more
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On the Hausdorff Dimension of Newhouse Phenomena [PDF]
Annales Henri Poincaré, 2015 We show that at the vicinity of a generic dissipative homoclinic unfolding of a surface diffeomorphism, the Hausdorff dimension of the set of parameters for which the diffeomorphism admits infinitely many periodic sinks is at least 1/2.
Berger, Pierre, De Simoi, Jacopo
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