Related papers: Dimension theory for linear solenoids
In this paper, we show that geometric Lorenz attractors have Hausdorff dimension strictly greater than $2$. We use this result to show that for a "large" set of real functions the Lagrange and Markov Dynamical spectrum associated to these…
Under fairly general assumptions, we prove that every compact invariant set $\mathcal I$ of the semiflow generated by the semilinear damped wave equation u_{tt}+\alpha u_t+\beta(x)u-\Deltau = f(x,u), (t,x)\in[0,+\infty[\times\Omega, u = 0,…
The goal of these notes is to give a brief explanation of how electric-magnetic duality in four dimensions is related to the existence of an unusual conformal field theory in six dimensions.
We refine the multifractal formalism for the local dimension of a Gibbs measure $\mu$ supported on the attractor $\Lambda$ of a conformal iterated functions system on the real line. Namely, for given $\alpha\in \mathbb{R}$, we establish the…
The primary objective of this paper is to investigate the modified Leray-alpha equation on the two-dimensional sphere $\mathbb{S}^2$, the square torus $\mathbb{T}^2$ and the three-torus $\mathbb{T}^3$. In the strategy, we prove the…
The attractor mechanism in five dimensional Einstein-Maxwell Chern-Simons theory is studied. The expression of the five dimensional rotating black object potential depending on Taub-NUT, electric and magnetic charges as well as on all the…
Let $\Lambda$ be an artinian ring. Generalizing the Loewy length, we propose the layer length associated with a torsion theory, which is a new measure for finitely generated $\Lambda$-modules.
The purpose of this paper is to investigate the existence and estimation of Hausdorff and fractal dimension of global attractors for a delayed reaction-diffusion equation on an unbounded domain. The noncompactness of the domain cause the…
Dimensional reduction of generalized gravity theories or string theories generically yields dilaton fields in the lower-dimensional effective theory. Thus at the level of D=4 theories, and cosmology many models contain more than just one…
This work is aimed by the spirit of 1946 Moran's Theorem, which ensures that both the box and the Hausdorff dimensions for any attractor could be calculated as the solution of an equation involving only its similarity factors. To achieve…
We study a wide class of fractal interpolation functions in a single platform by considering the domains of these functions as general attractors. We obtain lower and upper bounds of the box dimension of these functions in a more general…
An overview of some basic notions is given, especially with an eye towards somewhat "fractal" examples, such as infinite products of cyclic groups, p-adic numbers, and solenoids.
We investigate dimension-theoretic properties of concentric topological spheres, which are fractal sets emerging both in pure and applied mathematics. We calculate the box dimension and Assouad spectrum of such collections, and use them to…
In the scalar-tensor theory of gravitation it seems nontrivial to establish if solutions of the cosmological equations in the presence of a cosmological constant behave as attractors independently of the initial values. We develop a general…
Fractals are measurable metric sets with non-integer Hausdorff dimensions. If electric and magnetic fields are defined on fractal and do not exist outside of fractal in Euclidean space, then we can use the fractional generalization of the…
We derive a system with one degree of freedom that models a class of dynamical systems with strange attractors in three dimensions. This system retains all the characteristics of chaotic attractors and is expressed by a second-order…
We introduce the concept of solenoid as an abstract laminated space. We do a thorough study of solenoids, leading to the notion of ergodic and uniquely ergodic solenoids. We define generalized currents associated with immersions of oriented…
Currently only three spatial and one temporal dimensions are considered to be "physical". Recently, solutions to a plethora of questions have used the notion of extra-dimensions. The experimental verification of the existence of such extra…
We examine implications of angles having their own dimension, in the same sense as do lengths, masses, {\it etc.} The conventional practice in scientific applications involving trigonometric or exponential functions of angles is to assume…
We propose a theory in electromagnetic dynamics, in which time and space are equivalent with each other and have totally twelve dimensions. Then, we solve that with realistic assumptions and find a steady state as a solution. The solution…