Related papers: Renormalisable Henon-like Maps and Unbounded Geome…

We establish universality of the renormalised energy for mappings from a planar domain to a compact manifold, by approximating subquadratic polar convex functionals of the form $\int_\Omega f(|\mathrm{D} u|)\,\mathrm{d} x$. The analysis…

We consider random iteration of exponential entire functions, i.e. of the form ${\mathbb C}\ni z\mapsto f_\lambda(z):=\lambda e^z\in\mathbb C$, $\lambda\in{\mathbb C}\setminus \{0\}$. Assuming that $\lambda$ is in a bounded closed interval…

We consider C^{2} Henon-like families of diffeomorphisms of R^{2} and study the boundary of the region of parameter values for which the nonwandering set is uniformly hyperbolic. Assuming sufficient dissipativity, we show that the loss of…

In this paper, we study the limit measures of the empirical measures of Lebesgue almost every point in the basin of a partially hyperbolic attractor. They are strongly related to a notion named Gibbs u-state, which can be defined in a large…

We utilize Gaussian measure preserving systems to prove the existence and genericity of Lebesgue measure preserving transformations $T:[0,1]\rightarrow [0,1]$ which exhibit both mixing and rigidity behavior along families of asymptotically…

We consider the space $C_{\lambda}$ of all continuous interval maps preserving the Lebesgue measure $\lambda$. A continuous function $f\colon~[0,1]\to \mathbb R$ is called Besicovitch if it does not have any finite or infinite unilateral…

An ill-defined integral equation for modeling the mass-spectrum of mesons is regulated with an additional but unphysical parameter. This parameter dependance is removed by renormalization. Illustrative graphical examples are given.

For strongly dissipative H\'enon maps at the first bifurcation where the uniform hyperbolicity is destroyed by the formation of tangencies inside the limit set, we establish a thermodynamic formalism, i.e., prove the existence and…

It was recently shown that the harmonic measure is absolutely continuous with respect to the Hausdorff measure on a domain with an $n-1$ dimensional uniformly rectifiable boundary, in the presence of now well understood additional…

The present paper is devoted to the study of classes of mappings with non-bounded characteristic of quasiconformality. It is obtained a result on normal families of the open discrete mappings $f:D\rightarrow {\Bbb C}\setminus\{a, b\}$ of…

We proved that for the countably infinite number of one-parameterized one dimensional dynamical systems, they preserve the Lebesgue measure and they are ergodic for the measure (infinite ergodicity). Considered systems connect the parameter…

We develop a thermodynamic formalism for a strongly dissipative H\'enon-like map at the first bifurcation parameter at which the uniform hyperbolicity is destroyed by the formation of tangencies inside the limit set. For any $t\in\mathbb R$…

A classical theorem of Lusin states that all analytic sets are Lebesgue-measurable. In this article we established the reverse mathematical strength of Lusin's theorem, which depends on how precisely it is formalized. By doing so, we answer…

Consider the dynamical system constitued by a continuous function $F:\mathcal{A}^\mathbb{N}\to\mathcal{A}^\mathbb{N}$ where $\mathcal{A}$ is a finite alphabet. The perturbed counterpart, denoted by $F_\epsilon$, is obtained after each…

We construct a family of measures on $\bbR$ that are purely singular with respect to Lebesgue measure, and yet exhibit universal sine-kernel asymptotics in the bulk. The measures are best described via their Jacobi recursion coefficients:…

We consider some classes of piecewise expanding maps in finite dimensional spaces having invariant probability measures which are absolutely continuous with respect to Lebesgue measure. We derive an entropy formula for such measures and,…

Let $H$ be an infinite dimensional separable Hilbert space, $B(H)$ the $C^*$-algebra of all bounded linear operators on $H,$ $U(B(H))$ the unitary group of $B(H)$ and ${\cal K}\subset B(H)$ the ideal of compact operators. Let $G$ be a…

We prove that infinitely renormalizable contracting Lorenz maps with bounded geometry or the so-called {\it a priori bounds} satisfies the slow recurrence condition to the singular point $c$ at its two critical values $c_1^-$ and $c_1^+$.…

We prove an asymptotic normality guarantee for generalized low-rank matrix sensing -- i.e., matrix sensing under a general convex loss $\bar\ell(\langle X,M\rangle,y^*)$, where $M\in\mathbb{R}^{d\times d}$ is the unknown rank-$k$ matrix,…

In this paper, generalized metrics mean metrics taking values in general linearly ordered Abelian groups. Using the Hahn fields, we first prove that for every generalized metric space, if the set of the Archimedean equivalence classes of…