Related papers: A new class of $\alpha$-Farey maps and an applicat…

In this paper we consider a class of continued fraction expansions: the so-called $N$-expansions with a finite digit set, where $N\geq 2$ is an integer. These \emph{$N$-expansions with a finite digit set} were introduced in [KL,L], and…

In this paper we present a uniform way to derive families of maps from the corresponding differential equations describing systems which experience periodic kicks. The families depend on a single parameter - the order of a differential…

Let A_0, A_1 be nonnegative matrices in GL(n+1,Z) such that the subsimplexes A_0[Delta], A_1[Delta] split the standard unit n-dimensional simplex Delta in two. We prove that, for every n=1,2,... and up to the natural action of the symmetric…

We consider an analogue of Nakada's $\alpha$-continued fraction transformation in the setting of continued fractions with odd partial quotients. More precisely, given $\alpha \in [\frac{1}{2}(\sqrt{5}-1),\frac{1}{2}(\sqrt{5}+1)]$, we show…

We examine the structure of Farey maps, which are a class of maps (graph embeddings on surfaces) that have received significant attention recently. We describe how they are related to each other through regular coverings and parallel…

In this note, we study a family of subgraphs of the Farey graph, denoted as $\mathcal{F}_N$ for every $N\in\mathbb{N}.$ We show that $\mathcal{F}_N$ is connected if and only if $N$ is either equal to one or a prime power. We introduce a…

By means of singularisations and insertions in Nakada's alpha-expansions, which involves the removal of partial quotients 1 while introducing partial quotients with a minus sign, the natural extension of Nakada's continued fraction map…

We introduce a new, large class of continued fraction algorithms producing what are called contracted Farey expansions. These algorithms are defined by coupling two acceleration techniques -- induced transformations and contraction -- in…

We prove a conjecture of Calta, Kraaikamp and the author: For all $n\ge 3$, each member of their one-parameter family of interval maps, denoted $T_{3,n,\alpha}$, has its `first expansive return map' of natural extension given by the first…

For $\alpha\geq 2$, we investigate a class of Fourier extension operators on fractional surfaces $(\xi,|\xi|^\alpha)$. For the corresponding $\alpha$-Strichartz inequalities, by applying the missing mass method and bilinear restriction…

We discuss the asymptotic behaviour of random critical Boltzmann planar maps in which the degree of a typical face belongs to the domain of attraction of a stable law with index $\alpha \in (1,2]$. We prove that when conditioning such maps…

We investigate conditions for the extendibility of continuous algebra homomorphisms $\phi$ from the Fourier algebra $A(F)$ of a locally compact group $F$ to the Fourier-Stieltjes algebra $B(G)$ of a locally compact group $G$ to maps between…

In this paper we consider maps on the plane which are similar to quadratic maps in that they are degree 2 branched covers of the plane. In fact, consider for $\alpha$ fixed, maps $f_c$ which have the following form (in polar coordinates):…

We establish arithmetical properties and provide essential bounds for bi-sequences of approximation coefficients associated with the natural extension of maps, leading to continued fraction-like expansions. These maps are realized as the…

We construct a natural extension for each of Nakada's $\alpha$-continued fractions and show the continuity as a function of $\alpha$ of both the entropy and the measure of the natural extension domain with respect to the density function…

The main aim of the present paper is to introduce new classes of functions called $ \alpha $ $^m $ continuous maps and $ \alpha $ $^m $ irresolute maps. We obtain some characterizations of these classes and properties are studied.

We strengthen the standard bifurcation theorems for saddle-node, transcritical, pitchfork, and period-doubling bifurcations of maps. Our new formulation involves adding one or two extra terms to the standard truncated normal forms with…

We prove that large Boltzmann stable planar maps of index $\alpha \in (1;2)$ converge in the scaling limit towards a random compact metric space $\mathcal{S}_{\alpha}$ that we construct explicitly. They form a one-parameter family of random…

We describe Gauss-type maps as geometric realizations of certain codes in the monoid of nonnegative matrices in the extended modular group. Each such code, together with an appropriate choice of unimodular intervals in P^1R, determines a…

We present an unexpected connection between two map enumeration problems. The first one consists in counting planar maps with a boundary of prescribed length. The second one consists in counting planar maps with two points at a prescribed…