Related papers: Dimension theory for linear solenoids
We prove existence of the global attractor of the damped and driven 2D Euler--Bardina equations on the torus and give an explicit two-sided estimate of its dimension that is sharp as $\alpha\to0^+$.
The main goal of this paper has a double purpose. On the one hand, we propose a new definition in order to compute the fractal dimension of a subset respect to any fractal structure, which completes the theory of classical box-counting…
A \emph{fractal} is an object exhibiting complexity at arbitrarily small scales. In order to study and characterise fractals, one is often interested in quantifying how they fill up space on small scales. This gives rise to various notions…
The analytical solution of the three--dimensional linear pendulum in a rotating frame of reference is obtained, including Coriolis and centrifugal accelerations, and expressed in terms of initial conditions. This result offers the…
In this paper, we first prove an abstract theorem on the existence of polynomial attractors and the concrete estimate of their attractive velocity for infinite-dimensional dynamical systems, then apply this theorem to a class of wave…
Derrick's theorem is an important result that decides the existence of soliton configurations in field theories in different dimensions. It is proved using the extremization of finite energy of configurations under the scaling…
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 study dimensional properties of visible parts of fractal percolation in the plane. Provided that the dimension of the fractal percolation is at least 1, we show that, conditioned on non-extinction, almost surely all visible parts from…
For a finite partially ordered set we calculate the dimension of the variety of its subspace representations having fixed dimension vector. The dimension is given in terms of the Euler quadratic form associated with a partially ordered set,…
In this paper we introduce a notion of an attractor for local semiflows on topological spaces, which in some cases seems to be more suitable than the existing ones in the literature. Based on this notion we develop a basic attractor theory…
In this paper, exact Hausdorff dimension formulas for a class of self-affine attractors generated by affine Iterated Function Systems are derived. We consider systems containing an affine map whose $n$-th iterate is a similarity…
This article is devoted to the study of the existence of an exponential attractor for a family of problems, in which diffusion $d_{\lambda}$ blows up in localized regions inside the domain, \begin{equation*} \begin{cases} \displaystyle…
Axions arising as modes of higher-dimensional gauge fields are known to offer a compelling solution to the axion quality problem and to naturally arise in string theory. In this context, it is interesting to ask how we would interpret an…
Possible geometric frameworks for a unified theory of gravity and electromagnetism are investigated: General relativity is enlarged by allowing for an arbitrary complex linear connection and by constructing an extended spinor derivative…
\emph{Fractal percolation} or \emph{Mandelbrot percolation} is one of the most well studied families of random fractals. In this paper we study some of the geometric measure theoretical properties (dimension of projections and structure of…
The local theory of complex dimensions for real and $p$-adic fractal strings describes oscillations that are intrinsic to the geometry, dynamics and spectrum of archimedean and nonarchimedean fractal strings. We aim to develop a global…
We investigate the asymptotic behavior of the nonautonomous evolution problem generated by the Klein-Gordon equation in an expanding background, in one space dimension with periodic boundary conditions, with a nonlinear potential of…
We consider the theory of a symmetric tensor field in 4D, invariant under a subclass of infinitesimal diffeomorphism transformations, where the vector diff parameter is the 4-divergence of a scalar parameter. The resulting gauge symmetry…
This note provides a short guide to dimensional analysis in Lorentzian and general relativity and in differential geometry. It tries to revive Dorgelo and Schouten's notion of 'intrinsic' or 'absolute' dimension of a tensorial quantity. The…
A recent suggested definition of a relativistically correct three dimensional charge density of an extended hadron is shown to be physically and intuitively connected to an earlier relativistically correct two dimensional charge density…