Asymptotic behavior of a tagged particle in simple exclusion processesLandim, C.; Olla, S.; Varadhan, S.
doi: 10.1007/BF01241629pmid: N/A
We review in this article central limit theorems for a tagged particle in the simple exclusion process. In the first two sections we present a general method to prove central limit theorems for additive functional of Markov processes. These results are then applied to the case of a tagged particle in the exclusion process. Related questions, such as smoothness of the diffusion coefficient and finite dimensional approximations, are considered in the last section.
Maximal transitive sets with singularities for genericC 1 vector fieldsCarballo, C.; Morales, C.; Pacifico, M.
doi: 10.1007/BF01241631pmid: N/A
A transitive set Λ of a vector fieldX ismaximal transitive if it contains every transitive set ofX intersecting it. We shall prove that ifX isC
1 generic then every singularity ofX with either only one positive or only one negative eigenvalue belongs to a maximal transitive set ofX. In particular, we characterize maximal transitive sets with singularities for genericC
1 vector fields on closed 3-manifolds in terms of homoclinic classes associated to a unique singularity. We apply our results to the examples introduced in [3] and [15].
On the topology of foliations with a first integralMovasati, Hossein
doi: 10.1007/BF01241632pmid: N/A
The main objective of this article is to study the topology of the fibers of a generic rational function of the type
$$\frac{{F^p }}{{G^q }}$$
in the projective space of dimension two. We will prove that the action of the monodromy group on a single Lefschetz vanishing cycle δ generates the first homology group of a generic fiber of
$$\frac{{F^p }}{{G^q }}$$
. In particular, we will prove that for any two Lefschetz vanishing cyclesδ
0 andδ
1 in a regular compact fiber of
$$\frac{{F^p }}{{G^q }}$$
, there exists a mondromyh such thath(δ
0)=±δ
1.
AC 1 make or break lemmaHayashi, Shuhei
doi: 10.1007/BF01241633pmid: N/A
Mañé suggested the following question: Consider aC
r flow on a compact manifold without boundary and suppose that the ω-limit set of a pointp intersets the α-limit set ofq, i.e. ω(p)∩α(q)≠Ø. Can the flow beC
r-perturbed so that either (a)p is connected toq (p andq in the same orbit) or (b) ω(p)∩α(q)=Ø for the new flow? Here we solve positively a stronger version of this problem forC
1 small perturbations of the original flow.
Uniformization and the Poincaré metric on the leaves of a foliation by curvesNeto, A.
doi: 10.1007/BF01241634pmid: N/A
In this paper we prove that a holomorphic foliation by curves, on a complex compact manifoldM, whose singularities are non degenerated and whose tangent line bundle admits a metric of negative curvature, satisfies the following properties:(a): All leaves are hyperbolic.(b): The Poincaré metric on the leaves is continuous.(c): The set of uniformizations of the leaves by the Poincaré disc D is normal. Moreover, if (α
n
)
n
≥1 is a sequence of uniformizations which converges to a map α: D, then either α is a constant map (a singularity), or α is an uniformization of some leaf. This result generalizes Theorem B of [LN], in which we prove the same facts for foliations of degree ≥2 on projective spaces.