Results 1 to 10 of about 2,759 (172)

Packing and Hausdorff measures of stable trees [PDF]

, 2010
In this paper we discuss Hausdorff and packing measures of random continuous trees called stable trees. Stable trees form a specific class of L\'evy trees (introduced by Le Gall and Le Jan in 1998) that contains Aldous's continuum random tree (1991 ...
A Berlinkov, A Dress, B Haas, C Goldschmidt, C Rogers, DG Larman, DJ Aldous, DJ Aldous, G Edgar, G Miermont, G Miermont, H Haase, H Joyce, H Joyce, H Joyce, IS Helland, J Bertoin, J Lamperti, J-F Gall Le, J-F Gall Le, J-F Gall Le, M Gromov, M Jirina, M Silverstein, M Weill, NH Bingham, NH Bingham, R Abraham, S Evans, S Evans, S Taylor, T Duquesne, T Duquesne, T Duquesne, T Duquesne, T Duquesne   +35 more
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Generic zero-Hausdorff and one-packing spectral measures [PDF]

Journal of Mathematical Physics, 2021
For some metric spaces of self-adjoint operators, it is shown that the set of operators whose spectral measures have simultaneous zero upper-Hausdorff and one lower-packing dimension contains a dense Gδ subset. Applications include sets of limit-periodic operators.
Silas L. Carvalho, César R. de Oliveira
openaire   +2 more sources

Hausdorff and packing dimension of fibers and graphs of prevalent continuous maps [PDF]

, 2015
The notions of shyness and prevalence generalize the property of being zero and full Haar measure to arbitrary (not necessarily locally compact) Polish groups.
Balka, Richárd, Darji, Udayan B., Elekes, Márton   +2 more
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Classifying Cantor Sets by their Fractal Dimensions [PDF]

, 2010
In this article we study Cantor sets defined by monotone sequences, in the sense of Besicovitch and Taylor. We classify these Cantor sets in terms of their h-Hausdorff and h-Packing measures, for the family of dimension functions h, and characterize this
Cabrelli, Carlos A., Hare, Kathryn E., Molter, Ursula M.   +2 more
core   +3 more sources

Sixty Years of Fractal Projections [PDF]

, 2014
Sixty years ago, John Marstrand published a paper which, among other things, relates the Hausdorff dimension of a plane set to the dimensions of its orthogonal projections onto lines. For many years, the paper attracted very little attention.
A. Ferguson, A.S. Besicovitch, A.S. Besicovitch, A.S. Besicovitch, B.R. Hunt, B.R. Hunt, C. Tricot, D. Khoshnevisan, D.M. Oberlin, D.M. Oberlin, E. Järvanpää, E. Järvanpää, E. Järvanpää, F. Ledrappier, H. Furstenberg, H. Furstenberg, J. Barral, J. Bougain, J.C. Robinson, J.D. Howroyd, J.E. Hutchinson, K. Fässler, K.I. Eroğlu, K.J. Falconer, K.J. Falconer, K.J. Falconer, K.J. Falconer, K.J. Falconer, K.J. Falconer, K.J. Falconer, K.J. Falconer, M. Järvanpää, M. Leikas, M. Pollicott, M. Rams, M. Rams, M. Zähle, P. Erdős, P. Mattila, P. Mattila, P. Mattila, P. Mattila, P. Mattila, P. Shmerkin, R. Hovila, R. Hovila, R. Kaufman, R. Kaufman, R. Kenyon, R.O. Davies, R.O. Davies, T. Orponen, T. Orponen, T. Orponen, T.C. O’Neil, X. Hu, Y. Peres, Y. Peres, Y. Xiao, Z.M. Balogh, Z.M. Balogh   +60 more
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Hausdorff and packing measure for thick solenoids [PDF]

Studia Mathematica, 2004
Summary: For a linear solenoid with two different contraction coefficients and box dimension greater than 2, we give precise formulas for the Hausdorff and packing dimensions. We prove that the packing measure is infinite and give a condition necessary and sufficient for the Hausdorff measure to be positive, finite and equivalent to the SBR measure. We
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Hausdorff and packing dimensions and measures for nonlinear transversally non-conformal thin solenoids [PDF]

Ergodic Theory and Dynamical Systems, 2021
AbstractWe extend the results of Hasselblatt and Schmeling [Dimension product structure of hyperbolic sets. Modern Dynamical Systems and Applications. Eds. B. Hasselblatt, M. Brin and Y. Pesin. Cambridge University Press, New York, 2004, pp. 331–345] and of Rams and Simon [Hausdorff and packing measure for solenoids. Ergod. Th. & Dynam.
REZA MOHAMMADPOUR, FELIKS PRZYTYCKI, MICHAŁ RAMS   +2 more
openaire   +2 more sources

On random fractals with infinite branching: definition, measurability, dimensions [PDF]

, 2013
We discuss the definition and measurability questions of random fractals and find under certain conditions a formula for upper and lower Minkowski dimensions.
Berlinkov, Artemi
core   +3 more sources

Note on packing and weak-packing measures with Hausdorff functions

Journal of Mathematical Analysis and Applications, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wen, Sheng-You, Wen, Zhi-Ying
openaire   +1 more source

Dimension bounds for invariant measures of bi-Lipschitz iterated function systems [PDF]

, 2015
We study probabilistic iterated function systems (IFS), consisting of a finite or infinite number of average-contracting bi-Lipschitz maps on R^d. If our strong open set condition is also satisfied, we show that both upper and lower bounds for the ...
Anckar, Andreas
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