Related papers: The entropy of alpha-continued fractions: numerica…

We study the ergodic theory of a one-parameter family of interval maps T_alpha arising from generalized continued fraction algorithms. First of all, we prove the dependence of the metric entropy of T_alpha to be Hoelder-continuous in the…

We consider a class of simple one parameter families of interval maps, and we study how metric (resp. topological) entropy changes as the parameter varies. We show that in many cases the entropy displays a semi-regular behaviour, i.e. it is…

Two closely related families of ${\alpha}$-continued fractions were introduced in 1981: by Nakada on the one hand, by Tanaka and Ito on the other hand. The behavior of the entropy as a function of the parameter ${\alpha}$ has been studied…

We consider the family of piecewise linear maps $F(x,y)=\left(|x| - y + a, x - |y| + b\right),$ where $(a,b)\in \R^2$. In previous work, we identified a novel phenomenon: certain maps of this class possess one-dimensional invariant sets,…

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,…

We study an infinite family of one-parameter deformations, so-called $\alpha$-continued fractions, of interval maps associated to distinct triangle Fuchsian groups. In general for such one-parameter deformations, the function giving the…

We study the topological entropy of a two-parameter family of maps related to (a,b)-continued fraction algorithms and prove that it is constant on a square within the parameter space (two vertices of this square correspond to well-studied…

The entropy $h(T_\alpha)$ of $\alpha$-continued fraction transformations is known to be locally monotone outside a closed, totally disconnected set $\EE$. We will exploit the explicit description of the fractal structure of $\EE$ to…

We consider a one-parameter family of expanding interval maps $\{T_{\alpha}\}_{\alpha \in [0,1]}$ (japanese continued fractions) which include the Gauss map ($\alpha=1$) and the nearest integer and by-excess continued fraction maps…

Measuring the average information that is necessary to describe the behaviour of a dynamical system leads to a generalization of the Kolmogorov-Sinai entropy. This is particularly interesting when the system has null entropy and the…

Entropies are fundamental measures of uncertainty with central importance in information theory and statistics and applications across all the quantitative sciences. Under a natural set of operational axioms, the most general form of…

In this paper we consider continued fraction (CF) expansions on intervals different from $[0,1]$. For every $x$ in such interval we find a CF expansion with a finite number of possible digits. Using the natural extension, the density of the…

The notion of entropy appears in many fields and this paper is a survey about entropies in several branches of Mathematics. We are mainly concerned with the topological and the algebraic entropy in the context of continuous endomorphisms of…

Matrix-based centrality measures have enjoyed significant popularity in network analysis, in no small part due to our ability to rigorously analyze their behavior as parameters vary. Recent work has considered the relationship between…

The category of metric spaces is a subcategory of quasi-metric spaces. In this paper the notion of entropy for the continuous maps of a quasi-metric space is extended via spanning and separated sets. Moreover, two metric spaces that are…

We construct a countable family of open intervals contained in (0,1] whose endpoints are quadratic surds and such that their union is a full measure set. We then show that these intervals are precisely the monotonicity intervals of the…

We extend the results of our 2020 paper in the Annali della Scuola Normale Superiore di Pisa, Classe di Scienze. There, we associated to each of an infinite family of triangle Fuchsian groups a one-parameter family of continued fraction…

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…

We study the measure theoretic properties of typical C 0 maps of the interval. We prove that any ergodic measure is pseudo-physical, and conversely, any pseudo-physical measure is in the closure of the ergodic measures, as well as in the…

As a natural counterpart to Nakada's $\alpha$-continued fraction maps, we study a one-parameter family of continued fraction transformations with an indifferent fixed point. We prove that matching holds for Lebesgue almost every parameter…