Classical models of clusters’ fission have failed to fully explain strange phenomenons like the phenomenon of shattering (Ziff et al., 1987) and the sudden appearance of infinitely many particles in some systems with initial finite particles number. Furthermore, the bounded perturbation theorem presented in (Pazy, 1983) is not in general true in solution operators theory for models of fractional order γ (with 0 < γ ≤ 1). In this article, we introduce and study a model that can be understood as...

Soit $f$ un homéomorphisme du plan qui préserve l’orientation et qui a un point périodique $z^{*}$ de période $q\ge 2$. Nous montrons qu’il existe un point fixe $z$ tel que le nombre d’enlacement de $z^{*}$ et $z$ ne soit pas nul. En d’autres termes, le nombre de rotation de l’orbite de $z^{*}$ dans l’anneau ${ℝ}^2\setminus \left\{z\right\}$ est un élément non nul de $ℝ/\mathbb{Z}$. Ceci donne une réponse positive à une question posée par John Franks.

A groupoid is alternative if it satisfies the alternative laws $x\left(xy\right)=\left(xx\right)y$ and $x\left(yy\right)=\left(xy\right)y$. These laws induce four partial maps on ${\mathbb{N}}^{+}\times {\mathbb{N}}^{+}$$$(r,s)\mapsto ...$$

We show that a certain type of quasifinite, conservative, ergodic, measure preserving transformation always has a maximal zero entropy factor, generated by predictable sets. We also construct a conservative, ergodic, measure preserving transformation which is not quasifinite; and consider distribution asymptotics of information showing that e.g. for Boole's transformation, information is asymptotically mod-normal with normalization ∝ √n. Lastly, we show that certain ergodic, probability preserving...

The preperiodic dynatomic curve ${}_{n,p}$ is the closure in ℂ² of the set of (c,z) such that z is a preperiodic point of the polynomial $z\mapsto z^d+c$ with preperiod n and period p (n,p ≥ 1). We prove that each ${}_{n,p}$ has exactly d-1 irreducible components, which are all smooth and have pairwise transverse intersections at the singular points of ${}_{n,p}$. We also compute the genus of each component and the Galois group of the defining polynomial of ${}_{n,p}$.

We deal with a subshift of finite type and an equilibrium state μ for a Hölder continuous function. Let αⁿ be the partition into cylinders of length n. We compute (in particular we show the existence of the limit) $li{m}_{n\to \infty }{n}^{-1}log{\sum }_{j=0}^{\tau ₙ\left(x\right)}\mu \left(\alpha ⁿ\left(T^j\left(x\right)\right)\right)$, where $\alpha ⁿ\left(T^j\left(x\right)\right)$ is the element of the partition containing $T^j\left(x\right)$ and τₙ(x) is the return time of the trajectory of x to the cylinder αⁿ(x).

Early studies of the novel swine-origin 2009 influenza A (H1N1) epidemic indicate clinical attack rates in children much higher than in adults. Non-medical interventions such as school closings are constrained by their large socio-economic costs. Here we develop a mathematical model to ascertain the roles of pre-symptomatic influenza transmission as well as symptoms surveillance of children to assess the utility of school closures. Our model analysis...

This note brings a complement to the study of genericity of functions which are nowhere analytic mainly in a measure-theoretic sense. We extend this study to Gevrey classes of functions.

Let us consider the simplest model of one-dimensional probabilistic cellular automata (PCA). The cells are indexed by the integers, the alphabet is $\{0,1\}$, and all the cells evolve synchronously. The new content of a cell is randomly chosen, independently of the others, according to a distribution depending only on the content of the cell itself and of its right neighbor. There are necessary and sufficient conditions on the four parameters of such a PCA to have a Bernoulli product invariant measure....