entropie geometrique des feuilletages on definit et on etudie l entropie geometrique d un feuilletage generalisant directement l entropie topologique d un flot

poincare bendixson theory for leaves of codimension one the level of a local minimal set of a c2 codimension one foliation of a compact manifold is a nonnegative integer defined inductively level zero corresponding to the minimal sets in the usual sense each leaf of a local minimal set at level k is at level k the authors develop a theory of local minimal sets level and how leaves at level k asymptotically approach leaves at lower level this last generalizes the classical poincare bendixson theorem and provides information relating growth topological type and level e g if l is a totally proper leaf at level k then l has exactly polynomial growth of degree k and topological type k

markov property of point processes a point process mathcal n on r can be represented by the associated counting process t t r or by the associated sequence of jump times n n z and in accordance may possess two types of markov property the present paper first clarifies their mutual dependence leading in particular to the notion of weak multiplicativity for the joint distribution of two consecutive jump times then by means of results from a previous paper a uniquely determined markov variant tilde mathcal n is assigned to mathcal n without changing the one dimensional marginals this provides in particular a new characterization of the poisson process by these marginals and the adequate markov property further applications concern the explicit construction of the compensator and certain transition probabilities of tilde mathcal n

foliations the ergodic theorem and brownian motion regarding the leaves of a compact foliated riemannian manifold as the orbits of a dynamical system we will prove a birkhoff ergodic theorem asserting that the spatial average of a function equals its time average along random paths in the leaves there are several unexpected developments in the foundations first there always are measures on any compact foliated riemannian manifold m f with respect to which an adequate brownian motion along the leaves ergodic theorem holds second relative to these measures which are called harmonic there is a liouville type theorem for any bounded bore1 function on the manifold which is harmonic on each leaf namely for almost all leaves relative to any one of these harmonic measures this leaf harmonic function is constant on each leaf third the harmonic measures have a very reasonable local characterization in any foliation coordinate system they are transversal sums of h l dx l where h l is a positive harmonic function on the leaf l and dx l is the riemannian measure on l these statements comprise theorem 1 which is stated more precisely later in the introduction the first fact is surprising because up to now the only measures attached to foliations were the holonomy invariant transverse measures of plante 141 and ruelle sullivan 151 and some foliations do not admit these the second fact is unexpected because there are foliations where all the leaves are hyperbolic planes and each hyperbolic plane being conformal to the disk admits 285 0022 1236183 3 00

bounded pluriharmonic functions on symmetric irreducible siegel domains let cal d be an irreducible symmetric siegel domain and let s be a solvable group which acts simply transitively on cal d we exhibit three s invariant real second order degenerate elliptic operators bf l mathcal l bf h such that a bounded function f on mathcal d is pluriharmonic if and only if mathbf l f mathcal l f mathbf h f 0 the three operators are the same as in our former paper dhmp however there we needed a considerably stronger condition on f to derive the same conclusion

a note on the complexity function and entropy of pseudogroups abstract we examine the connections between complexity of a pseudogroup its equicontinuity the mixing property and entropy we prove that the entropy of a pseudogroup can be under some additional assumptions computed using a continuous and dynamically generating pseudometric

hua system and pluriharmonicity for symmetric irreducible siegel domains of type ii abstract we consider here a generalization of the hua system that was proved by johnson and koranyi to characterize poisson szego integrals for siegel domains of tube type we show that the situation is completely different when dealing with non tube type symmetric irreducible symmetric domains then all functions that are annihilated by this second order system and satisfy an h 2 type integrability condition are pluriharmonic functions

order conditioned independence of real random variables on considere un processus ponctuel sur r sans points multiples qui peut etre decrit par les temps d attente associes r 1 r 2 dans quel sens des variables aleatoires consecutives z n et z n11 peuvent elles etre independantes

equicontinuous foliated spaces riemannian foliations are characterized as those foliations whose holonomy pseudogroup consists of local isometries of a riemannian manifold their main structural features are well understood since the work of molina in this paper we analyze the more general concept of equicontinuous pseudogroup of homeomorphisms which gives rise to the notion of equicontinuous foliated space we show that equicontinuous foliated spaces have structural properties similar to those known for riemannian foliations the universal covers of their leaves are in the same quasi isometry class leaf closures are homogeneous spaces and the holonomy pseudogroup is indeed given by local isometries

a variational principle for free semigroup actions abstract in this paper we introduce a notion of measure theoretical entropy for a finitely generated free semigroup action and establish a variational principle when the semigroup is generated by continuous self maps on a compact metric space and has finite topological entropy in the case of semigroups generated by ruelle expanding maps we prove the existence of equilibrium states and describe some of their properties of independent interest are the different ways we will present to compute the metric entropy and a characterization of the stationary measures

black hole entropy topological entropy and the baum connes conjecture in k theory we shall try to exhibit a relation between black hole entropy and topological entropy using the famous baum connes conjecture for foliated manifolds which are particular examples of noncommutative spaces

nonexponential leaves at finite level abstracr previous examples of leaves with nonexponential and nonpolynomial growth due to g hector have occurred at infinite level here the same growth types are produced at finite level in open saturated sets of leaves without holonomy such sets consist of leaves with only one or two locally dense ends and it is shown that the exotic growth types only occur in the case of one locally dense end finally c foliations are produced with open saturated sets as above in which the leaves have strictly fractional growth

sur la dynamique unidimensionnelle en regularite intermediaire using probabilistic methods we prove new rigidity results for groups and pseudo groups of diffeomorphisms of one dimensional manifolds with intermediate regularity class i e between c 1 and c 2 in particular we show some generalizations of denjoy theorem and the classical kopell lemma for abelian groups these techniques are also applied to the study of codimension 1 foliations for instance we obtain several generalized versions of sacksteder theorem in class c 1 we conclude with some remarks about the stationary measure

on hardy bmo and lipschitz spaces of invariantly harmonic functions in the unit ball the invariantly harmonic functions in the unit ball bbb b n in bbb c n are those annihilated by the bergman laplacian delta the poisson szeg o kernel p z zeta solves the dirichlet problem for delta if f in c s n the poisson szeg o transform of f p f z int s n p z zeta f zeta d sigma zeta where d sigma is the normalized lebesgue measure on s n is the unique invariantly harmonic function u in bbb b n continuous up to the boundary such that u f on s n the poisson szeg o transform establishes loosely speaking a one to one correspondence between function theory in s n and invariantly harmonic function theory in bbb b n when n geq 2 it is natural to consider on s n function spaces related to its natural non isotropic metric for these are the spaces arising from complex analysis in the paper different characterizations of such spaces of smooth functions are given in terms of their invariantly harmonic extensions using maximal functions and area integrals as in the corresponding euclidean theory particular attention is given to characterization in terms of purely radial or purely tangential derivatives the smoothness is measured in two different scales that of sobolev spaces and that of lipschitz spaces including bmo and besov spaces 1991 mathematics subject classification 32a35 32a37 32m15 42b25

existence and non existence of length averages for foliations since the pioneering work of ghys et al it has been known that several methods of dynamical systems theory can be adopted to study of foliations our aim in this paper is to investigate complexity of foliations by generalising existence problem of time averages in dynamical systems theory to foliations it has recently been realised that a positive lebesgue measure set of points without time averages only appears for complicated dynamical systems such as dynamical systems with heteroclinic connections or homoclinic tangencies in this paper we introduce the concept of length averages to singular foliations and attempt to collect interesting examples with without length averages in particular we demonstrate that length averages exist everywhere for any codimension one mathscr c 1 orientable singular foliation without degenerate singularities on a compact surface under a mild condition on quasi minimal sets of the foliation which is in strong contrast to time averages of surface flows

soficity amenability and dynamical entropy in a previous paper the authors developed an operator algebraic approach to lewis bowen s sofic measure entropy that yields invariants for actions of countable sofic groups by homeomorphisms on a compact metrizable space and by measure preserving transformations on a standard probability space we show here that these measure and topological entropy invariants both coincide with their classical counterparts when the acting group is amenable

hyperbolic mean growth of bounded holomorphic functions in the ball we consider the hyperbolic hardy class q h p b 0 p it consists of holomorphic in the unit complex ball b for which 1 and sup q r 0 p d 0 r 1 b where q denotes the hyperbolic distance of the unit disc the hyperbolic version of the littlewood paley type g function and the area function are defined in terms of the invariant gradient of b and membership of qh p b is expressed by the l p property of the functions as an application we can characterize the boundedness and the compactness of the composition operator c defined by c f f o from the bloch space into the hardy space h p b

duality theorems for marginal problems given topological spaces x1 xn with product space x probability measures i on xi together with a real function h on x define a marginal problem as well as a dual problem using an extended version of choquet s theorem on capacities an analogue of the classical duality theorem of linear programming is established imposing only weak conditions on the topology of the spaces xi and the measurability resp boundedness of the function h applications concern among others measures with given support stochastic order and general marginal problems