Related papers: The L\'evy Map: A two-dimensional nonlinear map ch…
The configuration manifold $M$ of a mechanical system consisting of two unconstrained rigid bodies in $\mathbb{R}^n$, $n\geq 1$, is a manifold with boundary (typically with singularities.) A complete description of the system requires…
We revisit the Bieberbach conjecture in the framework of SLE processes and, more generally, L\'evy processes. The study of their unbounded whole-plane versions leads to a discrete series of exact results for the expectations of coefficients…
A new type of classical billiard - the Andreev billiard - is investigated using the tangent map technique. Andreev billiards consist of a normal region surrounded by a superconducting region. In contrast with previously studied billiards,…
We propose a model of card shuffling where a pack of cards, spread as points on a square table, are repeatedly gathered locally at random spots and then spread towards a random direction. A shuffling of the cards is then obtained by…
We compare two definitions of multistable L\'evy motions. Such processes are extensions of classical L\'evy motion where the stability index is allowed to vary in time. We show that the two multistable L\'evy motions have distinct…
We consider the Cauchy problem of 2+1 equivariant wave maps coupled to Einstein's equations of general relativity and prove that two separate (nonlinear) subclasses of the system disperse to their corresponding linearized equations in the…
We study L\'{e}vy-like and truncated L\'{e}vy-like flights with step probability distribution of the form $r^{-1+\nu}$ for negative, positive, and zero $\nu$, focusing on the appearance of fractal geometry characteristics in the generated…
In this paper we present a new local L\'evy Central Limit Theorem, showing convergence to stable states that are not necessarily the Gaussian, and use it to find new and intuitive entropically chaotic families with underlying one-particle…
For two-dimensional quantum billiards we derive the partial Weyl law, i.e. the average density of states, for a subset of eigenstates concentrating on an invariant region $\Gamma$ of phase space. The leading term is proportional to the area…
We propose a stochastic sampling approach to identify stability boundaries in general dynamical systems. The global landscape of Lyapunov exponent in multi-dimensional parameter space provides transition boundaries for stable/unstable…
Process convolutions yield random fields with flexible marginal distributions and dependence beyond Gaussianity, but statistical inference is often hampered by a lack of closed-form marginal distributions, and simulation-based inference may…
Pesin's identity provides a profound connection between entropy $h_{KS}$ (statistical mechanics) and the Lyapunov exponent $\lambda$ (chaos theory). It is well known that many systems exhibit sub-exponential separation of nearby…
This paper concerns the two-dimensional border-collision normal form -- a four-parameter family of piecewise-linear maps generalising the Lozi family and relevant to diverse applications. The normal form was recently shown to exhibit a…
A non-perturbative random-matrix theory is applied to the transmission of a monochromatic scalar wave through a disordered waveguide. The probability distributions of the transmittances T_{mn} and T_n=\sum_m T_{mn} of an incident mode n are…
The nonlinear dynamics of a recently derived generalized Lorenz model (Macek and Strumik, Phys. Rev. E 82, 027301, 2010) of magnetoconvection is studied. A bifurcation diagram is constructed as a function of the Rayleigh number where…
It is proved that the random integral mappings (some type of functionals of L\'evy processes) are always isomorphisms between convolution semigroups of infinitely divisible measures. However, the inverse mappings are no longer of the random…
This article study the class of distributions obtained by subordinating L\'evy processes and L\'evy bases. To do this we derive properties of a suitable mapping obtained via L\'evy mixing. We show that our results can be used to solve the…
We consider polyharmonic maps $\phi:(M,g)\rightarrow $\mathbb{E}^n$ of order k from a complete Riemannian manifold into the Euclidean space and let $p$ be a real constant satisfying $1<p<\infty$. (i) If, $\int_M|W^{k-1}|^p dv_g<\infty,$ and…
We discuss a two-parameter family of maps that generalize piecewise linear, expanding maps of the circle. One parameter measures the effect of a non-linearity which bends the branches of the linear map. The second parameter rotates points…
L\'evy walks (LWs) are spatiotemporally coupled random-walk processes describing superdiffusive heat conduction in solids, propagation of light in disordered optical materials, motion of molecular motors in living cells, or motion of…