Proposition de structures géométriques «amplifiées» pour le traitement des systèmes de points matériels
Propriétés arithmétiques et dynamiques du fractal de Rauzy
Dans ce travail, nous construisons explicitement deux isomorphismes métriques partout continus. L’un entre le système dynamique symbolique associé à la substitution et une rotation sur le tore ; l’autre, entre le système adique stationnaire [33] associé à la matrice de la substitution et la même rotation. Pour cela, nous étudions les propriétés arithmétiques de la frontière d’un ensemble compact de appelé “fractal de Rauzy”. Les constructions se généralisent aux substitutions de la forme ...
Propriétés combinatoires, ergodiques et arithmétiques de la substitution de Tribonacci
Nous étudions certaines propriétés combinatoires, ergodiques et arithmétiques du point fixe de la substitution de Tribonacci (introduite par G. Rauzy) et de la rotation du tore qui lui est associée. Nous établissons une généralisation géométrique du théorème des trois distances et donnons une formule explicite pour la fonction de récurrence du point fixe. Nous donnons des propriétés d’approximation diophantienne du vecteur de la rotation de : nous montrons, que pour une norme adaptée, la suite...
Propriétés dynamiques des régions d'instabilité
Propriétés ergodiques des mesures de Sinaï
Propriétés ergodiques du flot horocyclique d'une surface hyperbolique géométriquement finie
Propriétés ergodiques, en mesure infinie, de certains systèmes dynamiques fibrés
Propriétés générales des applications déviant la verticale
Proximality in Pisot tiling spaces
A substitution φ is strong Pisot if its abelianization matrix is nonsingular and all eigenvalues except the Perron-Frobenius eigenvalue have modulus less than one. For strong Pisot φ that satisfies a no cycle condition and for which the translation flow on the tiling space has pure discrete spectrum, we describe the collection of pairs of proximal tilings in in a natural way as a substitution tiling space. We show that if ψ is another such substitution, then and are homeomorphic if and...
Pruning theory and Thurston's classification of surface homeomorphisms
Two dynamical deformation theories are presented – one for surface homeomorphisms, called pruning, and another for graph endomorphisms, called kneading – both giving conditions under which all of the dynamics in an open set can be destroyed, while leaving the dynamics unchanged elsewhere. The theories are related to each other and to Thurston’s classification of surface homeomorphisms up to isotopy.
Prym Varieties and the Geodesic Flow on SO(n).
Prym-Tjurin varieties and the Hitchin map.
P-sets and minimal right ideals in ℕ*
Recall that a P-set is a closed set X such that the intersection of countably many neighborhoods of X is again a neighborhood of X. We show that if 𝔱 = 𝔠 then there is a minimal right ideal of (βℕ,+) that is also a P-set. We also show that the existence of such P-sets implies the existence of P-points; in particular, it is consistent with ZFC that no minimal right ideal is a P-set. As an application of these results, we prove that it is both consistent with and independent of ZFC that the shift...
Pseudo almost periodic and automorphic mild solutions to nonautonomous neutral partial evolution equations
In this work, we present a new concept of Stepanov weighted pseudo almost periodic and automorphic functions which is more generale than the classical one, and we obtain a new existence result of μ-pseudo almost periodic and μ-pseudo almost automorphic mild solutions for some nonautonomous evolution equations with Stepanov μ-pseudo almost periodic terms. An example is shown to illustrate our results.
Pseudo orbit tracing property and fixed points
If a continuous map f of a compact metric space has the pseudo orbit tracing property and is h-expansive then the set of all fixed points of f is totally disconnected.
Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three.
Pseudo-Markov transformations
Pseudo-self-affine tilings in .
Puiseux series polynomial dynamics and iteration of complex cubic polynomials
We let be the completion of the field of formal Puiseux series and study polynomials with coefficients in as dynamical systems. We give a complete description of the dynamical and parameter space of cubic polynomials in . We show that cubic polynomial dynamics over and are intimately related. More precisely, we establish that some elements of naturally correspond to the Fourier series of analytic almost periodic functions (in the sense of Bohr) which parametrize (near infinity) the quasiconformal...
Puissance extérieure d'un automate déterministe, application au calcul de la fonction zêta d'un système sofique