Related papers: Fractal uncertainty in higher dimensions

Using examples we test formulae previously conjectured to give the fractal information dimension of chaotic repellors and their stable and unstable manifolds in ``typical'' dynamical systems in terms of the Lyapunov exponents and the…

Fractons are exotic quasiparticles whose mobility in space is restricted by symmetries. In potential real-world realisations, fractons are likely lodged to a physical material rather than absolute space. Motivated by this, we propose and…

Nonlinear diffusion is studied in the presence of multiplicative noise. The nonlinearity can be viewed as a ``wall'' limiting the motion of the diffusing field. A dynamic phase transition occurs when the system ``unbinds'' from the wall.…

In Physics, we have laws that determine the time evolution of a given physical system, depending on its parameters and its initial conditions. When we have multi-stable systems, many attractors coexist so that their basins of attraction…

We build a bridge from density combinatorics to dimension theory of continued fractions. We establish a fractal transference principle that transfers common properties of subsets of $\mathbb N$ with positive upper density to properties of…

We prove a large deviations principle for the empirical law of the block sizes of a uniformly distributed non-crossing partition. As an application we obtain a variational formula for the maximum of the support of a compactly supported…

We introduce a new concept called as the mutual uncertainty between two observables in a given quantum state which enjoys similar features like the mutual information for two random variables. Further, we define the conditional uncertainty…

A new uncertainty relation (UR) is obtained for a system of N identical pure entangled particles if we use symmetrized observables when deriving the inequality. This new expression can be written in a form where we identify a term which…

We propose a new constructive model of the real continuum based on the notion of fractal definability. Rather than assuming the continuum as a completed uncountable totality, we view it as the cumulative result of a vast space of stratified…

Many mathematical models utilize limit processes. Continuous functions and the calculus, differential equations and topology, all are based on limits and continuity. However, when we perform measurements and computations, we can achieve…

We study the dynamics of a particle in a space that is non-differentiable. Non-smooth geometrical objects have an inherently probabilistic nature and, consequently, introduce stochasticity in the motion of a body that lives in their realm.…

Quasi one-dimensional systems are systems of particles in domains which are of infinite extent in one direction and of uniformly bounded size in all other directions, e.g. on a cylinder of infinite length. The main result proven here is…

We have built a new kind of manifolds which leads to an alternative new geometrical space. The study of the nowhere differentiable functions via a family of mean functions leads to a new characterization of this category of functions. A…

In this paper we consider extensions of the gradient elasticity models proposed earlier by the second author to describe materials with fractional non-locality and fractality using the techniques developed recently by the first author. We…

In this paper, we investigate the fractal uncertainty principle (FUP) for discrete Cantor sets, which are determined by an alphabet from a base of digits. Consider the base of M digits and the alphabets of cardinality A such that all the…

A variational principle is introduced to provide a new formulation and resolution for several boundary value problems with a variational structure. This principle allows one to deal with problems well beyond the weakly compact structure. As…

A class of simplified measures is constructed to capture the key features of generic spatio-temporally chaotic systems. A combined analytical and numerical investigation allows us to extablish the scaling beahviour of the fractal dimension…

When a corrosive solution reaches the limits of a solid sample, a chemical fracture occurs. An analytical theory for the probability of this chemical fracture is proposed and confirmed by extensive numerical experiments on a two dimensional…

We show that critical systems of finite size develop a fractal structure in momentum space with anomalous dimension given in terms of the isotherm critical exponent delta of the corresponding infinite system. The associated power laws of…

We entertain the idea that the uncertainty relation is not a principle, but rather it is a consequence of quantum mechanics. The uncertainty relation is then a probabilistic statement and can be clearly evaded in processes which occur with…