Results 41 to 50 of about 64,955 (216)
Hausdorff Dimension of Average Conformal Hyperbolic Sets [PDF]
, 2014 The Hausdorff dimension of a conformal repeller or conformal hyperbolic set is well understood. For non-conformal maps, the Hausdorff dimension is only known in some special cases.
Wright, Paul
core
Invariant Measure and Universality of the 2D Yang–Mills Langevin Dynamic
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We prove that the Yang–Mills (YM) measure for the trivial principal bundle over the two‐dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge‐fixing and Bourgain's method for invariant measures ...
Ilya Chevyrev, Hao Shen
wiley +1 more source
The Hausdorff dimension and exact Hausdorff measure of random recursive sets with overlapping
International Journal of Mathematics and Mathematical Sciences, 2002 We weaken the open set condition and define a finite intersection property in the construction of the random recursive sets. We prove that this larger class of random sets are fractals in the sense of Taylor, and give conditions when these sets have ...
Hongwen Guo, Dihe Hu
doaj +1 more source
Some Dimensional Results of a Class of Homogeneous Moran Sets
Journal of Mathematics, 2021 In this paper, we construct a class of special homogeneous Moran sets: mk-quasi-homogeneous perfect sets, and obtain the Hausdorff dimension of the sets under some conditions.
Jingru Zhang, Yanzhe Li, Manli Lou
doaj +1 more source
The Annals of Probability, 2004 We prove that the Hausdorff dimension of the trace of SLE_6 is almost surely 7/4 and give a more direct derivation of the result (due to Lawler-Schramm-Werner) that the dimension of its boundary is 4/3. We also prove that, for all <8, the SLE_ trace has cut-points.
openaire +4 more sources
Numerical studies of planar closed random walks
, 2008 Lattice numerical simulations for planar closed random walks and their winding sectors are presented. The frontiers of the random walks and of their winding sectors have a Hausdorff dimension $d_H=4/3$.
Comtet A +14 more
core +1 more source
Front Propagation Through a Perforated Wall
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We consider a bistable reaction– diffusion equation ut=Δu+f(u)$u_t=\Delta u +f(u)$ on RN${\mathbb {R}}^N$ in the presence of an obstacle K$K$, which is a wall of infinite span with many holes. More precisely, K$K$ is a closed subset of RN${\mathbb {R}}^N$ with smooth boundary such that its projection onto the x1$x_1$‐axis is bounded and that ...
Henri Berestycki +2 more
wiley +1 more source
Effective dimension in some general metric spaces [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 We introduce the concept of effective dimension for a general metric space. Effective dimension was defined by Lutz in (Lutz 2003) for Cantor space and has also been extended to Euclidean space.
Elvira Mayordomo
doaj +1 more source
Sierpiński Fractals and the Dimension of Their Laplacian Spectrum
Mathematical and Computational Applications, 2023 We establish rigorous estimates for the Hausdorff dimension of the spectra of Laplacians associated with Sierpiński lattices and infinite Sierpiński gaskets and other post-critically finite self-similar sets.
Mark Pollicott, Julia Slipantschuk
doaj +1 more source
Hausdorff dimension of three-period orbits in Birkhoff billiards
, 2011 We prove that the Hausdorff dimension of the set of three-period orbits in classical billiards is at most one. Moreover, if the set of three-period orbits has Hausdorff dimension one, then it has a tangent line at almost every point.Comment: 10 pages, 1 ...
Falconer K J +6 more
core +1 more source