Results 241 to 250 of about 3,791,283 (277)

Explicit ultimate bound sets of a new hyperchaotic system and its application in estimating the Hausdorff dimension

Nonlinear Dynamics, 2013
Pei Wang, Shaolin Tan, Li Wan
exaly   +2 more sources

Hausdorff dimension of planar self-affine sets and measures

Inventiones Mathematicae, 2017
Let $$X={\bigcup }{\varphi }_{i}X$$X=⋃φiX be a strongly separated self-affine set in $${\mathbb {R}}^2$$R2 (or one satisfying the strong open set condition).
B. Bárány, M. Hochman, Ariel Rapaport
semanticscholar   +1 more source

Additive energy and the Hausdorff dimension of the exceptional set in metric pair correlation problems

, 2016
For a sequence of integers {a(x)}x≥1 we show that the distribution of the pair correlations of the fractional parts of {〈αa(x)〉}x≥1 is asymptotically Poissonian for almost all α if the additive energy of truncations of the sequence has a power savings ...
C. Aistleitner, G. Larcher, Mark Lewko
semanticscholar   +1 more source

Hausdorff Dimension, Projections, Intersections, and Besicovitch Sets

New Trends in Applied Harmonic Analysis, Volume 2, 2017
This is a survey on recent developments on the Hausdorff dimension of projections and intersections for general subsets of Euclidean spaces, with an emphasis on estimates of the Hausdorff dimension of exceptional sets and on restricted projection ...
P. Mattila
semanticscholar   +1 more source

Hausdorff dimension of the graphs of the classical Weierstrass functions

, 2015
We show that the graph of the classical Weierstrass function $$\sum _{n=0}^\infty \lambda ^n \cos (2\pi b^n x)$$∑n=0∞λncos(2πbnx) has Hausdorff dimension $$2+\log \lambda /\log b$$2+logλ/logb, for every integer $$b\ge 2$$b≥2 and every $$\lambda \in (1/b ...
W. Shen
semanticscholar   +1 more source

Zero Hausdorff Dimension Spectrum for the Almost Mathieu Operator

, 2015
We study the almost Mathieu operator at critical coupling. We prove that there exists a dense $${G_\delta}$$Gδ set of frequencies for which the spectrum is of zero Hausdorff dimension.
Y. Last, M. Shamis
semanticscholar   +1 more source

Hausdorff Dimension and Non-degenerate Families of Projections

, 2012
We study parameterized families of orthogonal projections for which the dimension of the parameter space is strictly less than that of the Grassmann manifold.
E. Järvenpää, M. Järvenpää, T. Keleti   +2 more
semanticscholar   +1 more source

Hausdorff Dimension

The Krzyż Conjecture: Theory and Methods
Hausdorff dimension was singled out by Mandelbrot when he defined " fractal " as a set for which the Hausdorff dimension is strictly greater than the topological dimension. Before going through the details, let us agree with the following:

semanticscholar   +1 more source

Dirac Equation with Position-Dependent Mass and Coulomb-like Field in Hausdorff Dimension

, 2020
R. El-Nabulsi
semanticscholar   +1 more source

Fourier Analysis and Hausdorff Dimension

, 2015
P. Mattila
semanticscholar   +1 more source