Zobrazeno 1 - 10
of 51
pro vyhledávání: '"Zubrinic, Darko"'
In this paper we initiate the study of the box dimension of degenerate spiral trajectories of a class of ordinary differential equations. A class of singularities of focus type with two zero eigenvalues (nilpotent or more degenerate) has been studied
Externí odkaz:
http://arxiv.org/abs/2109.15167
Publikováno v:
Pure and Applied Functional Analysis, Volume 5, Number 5, 1073-1094, 2020
We study the essential singularities of geometric zeta functions $\zeta_{\mathcal L}$, associated with bounded fractal strings $\mathcal L$. For any three prescribed real numbers $D_{\infty}$, $D_1$ and $D$ in $[0,1]$, such that $D_{\infty}
Externí odkaz:
http://arxiv.org/abs/1908.07845
Publikováno v:
In Applied Mathematics and Computation 1 February 2023 438
We study polynomial planar systems with singularity of focus type without characteristic directions. Simple and natural transformation of weak focus has been used to obtain such degenerate focus. We compute the box dimension of a spiral trajectory, a
Externí odkaz:
http://arxiv.org/abs/1705.00372
We establish a Minkowski measurability criterion for a large class of relative fractal drums (or, in short, RFDs), in Euclidean spaces of arbitrary dimension in terms of their complex dimensions, which are defined as the poles of their associated fra
Externí odkaz:
http://arxiv.org/abs/1609.04498
Publikováno v:
J. Fractal Geom. 5 (2018), 1-119
We establish pointwise and distributional fractal tube formulas for a large class of relative fractal drums in Euclidean spaces of arbitrary dimensions. A relative fractal drum (or RFD, in short) is an ordered pair $(A,\Omega)$ of subsets of the Eucl
Externí odkaz:
http://arxiv.org/abs/1604.08014
Publikováno v:
Dissertationes mathematicae, 526 (2017) 1-105
In 2009, the first author introduced a new class of zeta functions, called `distance zeta functions', associated with arbitrary compact fractal subsets of Euclidean spaces of arbitrary dimension. It represents a natural, but nontrivial extension of t
Externí odkaz:
http://arxiv.org/abs/1603.00946
Publikováno v:
J. Math. Anal. Appl. 453 (2017), 458-484
We study meromorphic extensions of distance and tube zeta functions, as well as of geometric zeta functions of fractal strings. The distance zeta function $\zeta_A(s):=\int_{A_\delta} d(x,A)^{s-N}\mathrm{d}x$, where $\delta>0$ is fixed and $d(x,A)$ d
Externí odkaz:
http://arxiv.org/abs/1508.04784
Publikováno v:
Adv. in Math. 307 (2017), 1215-1267
Recently, the first author has extended the definition of the zeta function associated with fractal strings to arbitrary bounded subsets $A$ of the $N$-dimensional Euclidean space ${\mathbb R}^N$, for any integer $N\ge1$. It is defined by $\zeta_A(s)
Externí odkaz:
http://arxiv.org/abs/1506.03525
Publikováno v:
Fractal analysis of Hopf bifurcation at infinity, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 22(2012), 1230043-1-1230043-15
Using geometric inversion with respect to the origin we extend the definition of box dimension to the case of unbounded subsets of Euclidean spaces. Alternative but equivalent definition is provided using stereographic projection on the Riemann spher
Externí odkaz:
http://arxiv.org/abs/1502.03009