Related papers: Masur's Divergence for Tori and Kummer Surfaces

We introduce the notion of equivariant basic cohomology for singular Riemannian foliations with transverse infinitesimal actions, and prove some elementary properties such as its invariance under homotopies. For the particular case of…

We adjust Arnoux's coding, in terms of regular continued fractions, of the geodesic flow on the modular surface to give a cross section on which the return map is a double cover of the natural extension for the \alpha-continued fractions,…

On the unit tangent bundle of a nonflat compact nonpositively curved surface, we prove that there is a unique probability Borel measure invariant by a horocyclic flow which gives full measure to the set of rank $1$ vectors recurrent by the…

In this work we study the geometric properties of spacelike foliations by hypersurfaces on a Lorentz manifold. We find an equation that relates the foliation with the ambient manifold and apply it to investigate conditions for the leaves…

We consider diffeomorphisms in the $C^\infty$-closure of the conjugancy class of translations of the 2-torus. By a theorem of Fathi and Herman, a generic diffeomorphism in that space is minimal and uniquely ergodic. We define a new…

We prove that a one-dimensional foliation with generic singularities on a projective space, exhibiting a Lie group transverse structure in the complement of some codimension one algebraic subset is logarithmic, i.e., it is the intersection…

Following Beck-Chen, we say a flow $\phi_t$ on a metric space $(X, d)$ is superdense if there is a $c > 0$ such that for every $x \in X$, and every $T>0$, the trajectory $\{\phi_t x\}_{0 \le t \le cT}$ is $1/T$-dense in $X$. We show that a…

We prove a general result about the short time existence and uniqueness of second order geometric flows transverse to a Riemannian foliation on a compact manifold. Our result includes some flows already existing in literature, as the…

We show that on any compact Riemann surface with variable negative curvature there exists a measure which is invariant and ergodic under the geodesic flow and whose projection to the base manifold is 2-dimensional and singular with respect…

The leafwise cohomology of the weak stable foliation of the geodesic flows is very important in the study of the space of actions whose orbit foliation is the weak stable foliation of geodesic flows.The dimension one cohomology was computed…

We study the geodesic flow on the normal line congruence of a minimal surface in ${\Bbb{R}}^3$ induced by the neutral K\"ahler metric on the space of oriented lines. The metric is lorentz with isolated degenerate points and the flow is…

A 3-manifold is foliar if it supports a codimension-one co-oriented taut foliation. Suppose $M$ is an oriented 3-manifold with connected boundary a torus, and suppose $M$ contains a properly embedded, compact, oriented, surface $R$ with a…

We relate ergodic-theoretic properties of a very small tree or lamination to the behavior of folding and unfolding paths in Outer space that approximate it, and we obtain a criterion for unique ergodicity in both cases. Our main result is…

We give a short proof of the unique ergodicity of the strong stable foliation of the geodesic flow on the frame bundle of a hyperbolic manifold admitting a finite measure of maximal entropy. Equivalently, let G = S0o(n, 1), $\Gamma$…

An asymptotic expansion is established for time averages of translation flows on flat surfaces. This result, which extends earlier work of A.Zorich and G.Forni, yields limit theorems for translation flows. The argument, close in spirit to…

We define a class of nonsingular holomorphic foliations on compact complex tori which generalizes (in higher codimension) the turbulent foliations of codimension one constructed by Ghys. For those smooth turbulent foliations we prove that…

We prove that a surface carries a hexagonal 3-web of geodesics if and only if the geodesic flow on the surface admits a cubic first integral and show that the system of partial differential equations, governing metrics on such surfaces, is…

We consider constant mean curvature surfaces (invariant by a continuous group of isometries) lying at bounded distance from a horizontal geodesic on any homogeneous $3$-manifold $\mathbb{E}(\kappa,\tau)$ with isometry group of dimension…

We consider a singular holomorphic foliation $\uF$ defined near a compact curve $\uC$ of a complex surface. Under some hypothesis on $(\uF,\uC)$ we prove that there exists a system of tubular neighborhoods $U$ of a curve $\underline{\mc D}$…

We establish exponential mixing for the geodesic flow $\varphi_t\colon T^1S\to T^1S$ of an incomplete, negatively curved surface $S$ with cusp-like singularities of a prescribed order. As a consequence, we obtain that the Weil-Petersson…