Related papers: A parameter ASIP for the quadratic family

Let $A_1, \ldots, A_r$ be Hermitian $n \times n$ matrices and $S = \sum A_i \otimes s_i$ the associated matrix semicircle, where $s_1, \ldots, s_r$ are free semicircular variables. We prove that the following are equivalent: (i) the matrix…

Chaos thresholds of the $z$-logistic maps $x_{t+1}=1-a|x_t|^z$ $(z>1; t=0,1,2,...)$ are numerically analysed at accumulation points of cycles 2, 3 and 5. We verify that the nonextensive $q$-generalization of a Pesin-like identity is…

Clemm and Trebat-Leder (2014) proved that the number of quadratic number fields with absolute discriminant bounded by $x$ over which there exist elliptic curves with good reduction everywhere and rational $j$-invariant is $\gg…

In this paper we show two results. In the first result we consider $\lambda_n-n=\frac{A}{n^\alpha}$ for $n\in\mathbb N$; if $\alpha>1/2$ and $0<A<\frac{1}{\pi\sqrt{2 \sqrt{2}\zeta(2\alpha)}}$, the system $\left\{\operatorname{sinc}(…

A sufficient geometrical condition for the existence of absolutely continuous invariant probability measures for S-unimodal maps will be discussed. The Lebesgue typical existence of such measures in the quadratic family will be a…

We show that for the standard map family, for all values of the parameter, except one, the mapping has positive topological entropy. The main tool is the following result. Let $S$ be a compact connected orientable surface and $f:S…

In this paper, we consider a Borel measurable map of a compact metric space which admits an inducing scheme. Under the finite weighted complexity condition, we establish a thermodynamic formalism for a parameter family of potentials…

We show that for $0<\gamma, \gamma' <1$ and for measurable subsets of the unit square with Lebesgue measure $\gamma$ there exist bi-Lipschitz maps with bounded Lipschitz constant (uniformly over all such sets) which are identity on the…

In the first part, we construct a cut and project scheme from a family $\{P_\varepsilon\}$ of sets verifying four conditions. We use this construction to characterize weighted Dirac combs defined by cut and project schemes and by continuous…

Let $(X,d,f)$ be a dynamical system, where $(X,d)$ is a compact metric space and $f:X\rightarrow X$ is a continuous map. Using the concepts of \textit{g-almost product property} and \textit{uniform separation property} introduced by Pfister…

Let $A(s) = \sum_n a_n n^{-s}$ be a Dirichlet series admitting meromorphic continuation to the complex plane. Assume we know the location of the poles of $A(s)$ with $|\Im s| \leq T$, and their residues, for some large constant $T$. It is…

We introduce a family of rings of symmetric functions depending on an infinite sequence of parameters. A distinguished basis of such a ring is comprised by analogues of the Schur functions. The corresponding structure coefficients are…

Let $p\equiv 1 \pmod{4}$ be a prime. Write $t = \prod_{x=1}^{(p-1)/2}x$. Since $t ^2\equiv -1 \pmod{p}$ , we can divide $\{1,2,\ldots,(p-1)/2\}$ into $(p-1)/4$ ordered pairs so that each pair, say $<a,\tilde{a}>$ , satisfies that $t a…

We develop an elementary method for proving the PBW theorem for associative algebras with an ascending filtration. The idea is roughly the following. At first, we deduce a proof of the PBW property for the {\it ascending} filtration (with…

Let $\varphi$ be a univalent non-elliptic self-map of the unit disc $\mathbb D$ and let $(\psi_{t})$ be a continuous one-parameter semigroup of holomorphic functions in $\mathbb D$ such that $\psi_{1}\neq\mathrm{id}_{\mathbb D}$ commutes…

Fix $\delta\in(0,1]$, $\sigma_0\in[0,1)$ and a real-valued function $\varepsilon(x)$ for which $\limsup_{x\to\infty}\varepsilon(x)\le 0$. For every set of primes ${\mathcal P}$ whose counting function $\pi_{\mathcal P}(x)$ satisfies an…

We consider the asymmetric simple exclusion process (ASEP) on $\mathbb{Z}$. For continuous densities, ASEP is in local equilibrium for large times, at discontinuities however, one expects to see a dynamical phase transition, i.e. a mixture…

In this paper, we first show that any nonlinear monotonic increasing contracting maps with one discontinuous point on a unit interval which has an unique periodic point with period $n$ conjugates to a piecewise linear contracting map which…

We define the quantile set of order $\alpha \in \left[ 1/2,1\right) $ associated to a law $P$ on $\mathbb{R}^{d}$ to be the collection of its directional quantiles seen from an observer $O\in \mathbb{R}^{d}$. Under minimal assumptions these…

We consider the space $A(\mathbb{T}^d)$ of absolutely convergent Fourier series on the torus $\mathbb{T}^d$. The norm on $A(\mathbb{T}^d)$ is naturally defined by $\|f\|_{A}=\|\widehat{f}\|_{l^1}$, where $\widehat{f}$ is the Fourier…