Powers and alternative laws
A groupoid is alternative if it satisfies the alternative laws and . These laws induce four partial maps on
Powers of positive polynomials and codings of Markov chains onto Bernoulli shifts.
Precise counting results for closed orbits of Anosov flows
Predictability, entropy and information of infinite transformations
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...
Preperiodic dynatomic curves for
The preperiodic dynatomic curve is the closure in ℂ² of the set of (c,z) such that z is a preperiodic point of the polynomial with preperiod n and period p (n,p ≥ 1). We prove that each has exactly d-1 irreducible components, which are all smooth and have pairwise transverse intersections at the singular points of . We also compute the genus of each component and the Galois group of the defining polynomial of .
Presentations of subshifts and their topological conjugacy invariants.
Pressure and recurrence
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) , where is the element of the partition containing and τₙ(x) is the return time of the trajectory of x to the cylinder αⁿ(x).
Presymplectic lagrangian systems. I : the constraint algorithm and the equivalence theorem
Presymplectic lagrangian systems. II : the second-order equation problem
Pre-symptomatic Influenza Transmission, Surveillance, and School Closings: Implications for Novel Influenza A (H1N1)
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...
Prevalence of non-Lipschitz Anosov foliations.
Prevalence of "nowhere analyticity"
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.
Prime Orbit Theorems with Multi-Dimensional Constraints for Axiom A Flows.
Probabilistic cellular automata and random fields with i.i.d. directions
Let us consider the simplest model of one-dimensional probabilistic cellular automata (PCA). The cells are indexed by the integers, the alphabet is , 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....
Probabilistic finite state automata and time series analysis.
Probabilistic well-posedness for the cubic wave equation
The purpose of this article is to introduce for dispersive partial differential equations with random initial data, the notion of well-posedness (in the Hadamard-probabilistic sense). We restrict the study to one of the simplest examples of such equations: the periodic cubic semi-linear wave equation. Our contributions in this work are twofold: first we break the algebraic rigidity involved in our previous works and allow much more general randomizations (general infinite product measures v.s. Gibbs...
Problèmes de modules pour des équations différentielles non linéaires du premier ordre
Problèmes d'intersections et de points fixes en géométrie hamiltonienne.
Problèmes elliptiques, surfaces de Riemann et structures symplectiques
Problems and solutions by the application of Julia set theory to one-dot and multi-dots numerical methods.