相关论文: Happy fractals and some aspects of analysis on met…
We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a…
We present a construction, called the limit of a tree system of spaces (or, less formally, a tree of spaces). The construction is designed to produce compact metric spaces that resemble fractals, out of more regular spaces, such as closed…
Fractional integral operators connected with real-valued scalar functions of matrix argument are applied in problems of mathematics, statistics and natural sciences. In this article we start considering the case of a Gauss hypergeometric…
We introduce the fractal expansions, sequences of integers associated to a number. We show that these sequences characterize the O-sequences and encode some information on lex segment ideals. Moreover, we introduce a numerical functions…
We perform fractal analysis on a closed classical hard-wall billiard, the circular billiard with a straight cut, assuming there are two openings on the boundary. We use a two-dimensional set of initial conditions that produce all possible…
Fractal Clifford Spaces (FCS) may be considered as a challenging approach to the unification of micro-physics and macro-physics. Trajectories of these manifolds are described by different poly-vectors describing paths and their deviation…
Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate…
A quantum fractal is a wavefunction with a real and an imaginary part continuous everywhere, but differentiable nowhere. This lack of differentiability has been used as an argument to deny the general validity of Bohmian mechanics (and…
A mapping $f:X\to Y$ between metric spaces is called \emph{little Lipschitz} if the quantity $$ \operatorname{lip}(f(x)=\liminf_{r\to0}\frac{\operatorname{diam} f(B(x,r))}{r} $$ is finite for every $x\in X$. We prove that if a compact (or,…
We analyse the relationship between different extremal notions in Lipschitz free spaces (strongly exposed, exposed, preserved extreme and extreme points). We prove in particular that every preserved extreme point of the unit ball is also a…
The topological and metrical equivalence of fractals is an important topic in analysis. In this paper, we use a class of finite state automata, called $\Sigma$-automaton, to construct psuedo-metric spaces, and then apply them to the study…
If our aesthetic preferences are affected by fractal geometry of nature, scaling regularities would be expected to appear in all art forms, including music. While a variety of statistical tools have been proposed to analyze time series in…
For fixed natural numbers $r$ and $s$, where $2\leq s \leq r$, we consider a representation of numbers from the interval $[0;\frac{r}{s-1}]$ obtained by encoding numbers by means of the alphabet $A=\{0,1,...,r\}$ via the expansion…
Fractals and quasiperiodic structures share self-similarity as a structural property. Motivated by the link between Fibonacci fractals and quasicrystals which are scaled by the golden mean ratio $\frac{1+\sqrt{5}}{2}$, we introduce and…
Fractal sets, by definition, are non-differentiable, however their dimension can be continuous, differentiable, and arithmetically manipulable as function of their construction parameters. A new arithmetic for fractal dimension of polyadic…
We determine the scaling properties of geometric operators such as lengths, areas, and volumes in models of higher derivative quantum gravity by renormalizing appropriate composite operators. We use these results to deduce the fractal…
Recently a stochastic underpinning for space time has been considered, what may be called Quantized Fractal Space Time. This leads us to a number of very interesting consequences which are testable, and also provides a rationale for several…
For a Borel measure on the unit interval and a sequence of scales that tend to zero, we define a one-parameter family of zeta functions called multifractal zeta functions. These functions are a first attempt to associate a zeta function to…
Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets…
There exists a variety of physically interesting situations described by continuous maps that are nondifferentiable on some surface in phase space. Such systems exhibit novel types of bifurcations in which multiple coexisting attractors can…