On the hausdorff dimensions of distance sets
Web7 de abr. de 2024 · Keich (1999) showed that the sharp gauge function for the generalized Hausdorff dimension of Besicovitch sets in is between and by refining an argument of Bourgain (1991). It is not known whether the iterated logarithms in … WebIn mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff. …
On the hausdorff dimensions of distance sets
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Web20 de jun. de 2024 · Their estimate also works on the Hausdorff dimension of distance sets (see [4], [13]). ... On Hausdorff dimension of radial projections Preprint Mar 2024 Bochen Liu View Show abstract... Web4 de jul. de 2024 · We prove new bounds on the dimensions of distance sets and pinned distance sets of planar sets. Among other results, we show that if \(A\subset {\mathbb …
Web17 de mar. de 2016 · In this paper, we replace the Hausdorff dimension on the left hand side of the first inequality above by the lower Minkowski dimension and replace the Lebesgue measure of the set of translates by a Hausdorff measure on a set of sufficiently large ... On the Hausdorff dimensions of distance sets, Mathematika 32 (1985), … Web10 de abr. de 2024 · Fractal dimensions give you an intuition about the geometry of a set. Having identified some interesting random sets and possible ways to measure them, we note that such studies can be traced to the pioneering work of Lévy [30] and Taylor [47], [48], [49] on the sample path properties of the Brownian motion. We refer the reader to …
Web26 de jan. de 2024 · We prove new bounds on the dimensions of distance sets and pinned distance sets of planar sets. Among other results, we show that if is a Borel set of Hausdorff dimension , then its distance set has Hausdorff dimension at least . WebJ., Bourgain [1994] Hausdorff dimension and distance sets, Israel J. Math. 87, 193–201. J., Bourgain [1995] Some new estimates on oscillatory integrals, in Essays on Fourier Analysis in Honor of Elias M. Stein, Princeton University Press, 83–112.
WebOn the Hyperbolic Hausdorff Dimension of the Boundary of a Basin of Attraction for a Holomorphic Map and of Quasirepellers . × Close Log In. Log in with Facebook Log in …
WebThis verifies a strong variant of Falconer's distance set conjecture for sets of equal Hausdorff and packing dimension, outside the endpoint $s=1$. We prove that if $A$ is … shugghead gamingWeb23 de mai. de 2024 · Editorial introduction. On distance sets, box-counting and Ahlfors-regular sets, Discrete Analysis 2024:9, 22 pp. A well-known problem of Falconer, a sort of continuous analogue of the Erdős distinct-distance problem, asks how large the Hausdorff dimension of a Borel subset of R d needs to be before the set of distances between … shuggard box port marlyWeb18 de out. de 2024 · arXivLabs: experimental projects with community collaborators. arXivLabs is a framework that allows collaborators to develop and share new arXiv … shugg electricalWeb18 de out. de 2024 · The main topics concern applications of the Fourier transform to geometric problems involving Hausdorff dimension, such as Marstrand type projection … the otterbox warrantyWebIn [DU2] the dynamical dimension of the Julia set J = J(f ) for a rational function f was introduced and defined as follows (0.2) HDmhyp (J) = sup{HD(µ) : µ is an ergodic probability f -invariant measure of positive Lyapunov exponent}, where HD(µ) is the infimum of Hausdorff dimensions of sets of full measure µ (mhyp abbreviates, measure hyperbolic). shuggie bain book group questionsWebAccording to a result of K. Falconer (1985), the setD(A)={ x−y ;x, y ∈A} of distances for a Souslin setA of ℝ n has positive 1-dimensional measure provided the Hausdorff … shuggazoom cityWeb17 de abr. de 2024 · We prove that if A is a Borel set in the plane of equal Hausdorff and packing dimension s > 1, then the set of pinned distances { x − y : y ∈ A} has full … shuggie bain audiobook free download