Zobrazeno 1 - 10
of 295
pro vyhledávání: '"Strichartz, Robert S."'
We study the graphs associated with Vicsek sets in higher dimensional settings. First, we study the eigenvalues of the Laplacians on the approximating graphs of the Vicsek sets, finding a general spectral decimation function. This is an extension of
Externí odkaz:
http://arxiv.org/abs/2104.11837
We study the balanced resistance forms on the Julia sets of Misiurewicz-Sierpinski maps, which are self-similar resistance forms with equal weights. In particular, we use a theorem of Sabot to prove the existence and uniqueness of balanced forms on t
Externí odkaz:
http://arxiv.org/abs/2008.07065
The study of Julia sets gives a new and natural way to look at fractals. When mathematicians investigated the special class of Misiurewicz's rational maps, they found out that there is a Julia set which is homeomorphic to a well known fractal, the Si
Externí odkaz:
http://arxiv.org/abs/2001.03821
We study the spectrum of the Laplacian on the Sierpinski lattices. First, we show that the spectrum of the Laplacian, as a subset of $\mathbb{C}$, remains the same for any $\ell^p$ spaces. Second, we characterize all the spectral points for the latti
Externí odkaz:
http://arxiv.org/abs/1910.01771
We construct a surface that is obtained from the octahedron by pushing out 4 of the faces so that the curvature is supported in a copy of the Sierpinski gasket in each of them, and is essentially the self similar measure on SG. We then compute the bo
Externí odkaz:
http://arxiv.org/abs/1907.06265
We give a discrete characterization of the trace of a class of Sobolev spaces on the Sierpinski gasket to the bottom line. This includes the L2 domain of the Laplacian as a special case. In addition, for Sobolev spaces of low orders, including the do
Externí odkaz:
http://arxiv.org/abs/1905.03391
One of the well-studied equations in the theory of ODEs is the Mathieu differential equation. A common approach for obtaining solutions is to seek solutions via Fourier series by converting the equation into an infinite system of linear equations for
Externí odkaz:
http://arxiv.org/abs/1904.00950
We present eigenvalue data and pictures of eigenfunctions of the classic and quadratic snowflake fractal and of quadratic filled Julia sets. Furthermore, we approximate the area and box-counting dimension of selected Julia sets to compare the eigenva
Externí odkaz:
http://arxiv.org/abs/1903.08259
We study several variants of the classical Sierpinski Carpet (SC) fractal. The main examples we call infinite magic carpets (IMC), obtained by taking an infinite blowup of a discrete graph approximation to SC and identifying edges using torus, Klein
Externí odkaz:
http://arxiv.org/abs/1902.03408