相关论文: A construction of pseudo-Anosov homeomorphisms usi…

We show that the identity component of the group of diffeomorphisms of a closed oriented surface of positive genus admits many unbounded quasi-morphisms. As a corollary, we also deduce that this group is not uniformly perfect and its…

We define new topological invariants for Anosov representations and study them in detail for maximal representations of the fundamental group of a closed oriented surface into the symplectic group.

In this paper, we propose crossing statistics and its generalization, as a new framework to characterize the anisotropy in a 2D field, e.g. height on a surface, extendable to higher dimensions. By measuring $\nu^+$, the number of…

In this paper, we give sufficient conditions for a Perron number, given as the leading eigenvalue of an aperiodic matrix, to be a pseudo-Anosov dilatation of a compact surface. We give an explicit construction of the surface and the map…

We show that the Nielsen-Thurston classification of mapping classes of the sphere with four marked points is determined by the quantum SU(n)-representations, for any fixed integer $n \geq 2$. In the Pseudo-Anosov case we also show that the…

We show that every pseudo-Anosov flow on a graph manifold is almost equivalent, i.e. orbit equivalent in the complement of a finite collection of closed orbits, to a totally periodic pseudo-Anosov flow or a suspension Anosov flow. The proof…

Let $M$ be a closed 3-manifold which admits an Anosov flow. In this paper we develop a technique for constructing partially hyperbolic representatives in many mapping classes of $M$. We apply this technique both in the setting of geodesic…

We study circle extensions of analytic Anosov maps on the two torus: these are examples of partially hyperbolic maps for which the qualitative ergodic theory is well understood. In this paper we investigate rates of mixing (for the SRB…

We study quasi-morphisms on the groups Pn of pure braids on n strings and on the group D of compactly supported area-preserving diffeomorphisms of an open two-dimensional disc. We show that it is possible to build quasi-morphisms on Pn by…

We prove a result allowing to build (transitive or non-transitive) Anosov flows on 3-manifolds by gluing together filtrating neighborhoods of hyperbolic sets. We give several applications; for example: 1. we build a 3-manifold supporting…

In this article we analyze totally periodic pseudo-Anosov flows in graph three manifolds. This means that in each Seifert fibered piece of the torus decomposition, the free homotopy class of regular fibers has a finite power which is also a…

Let $F',F$ be any two closed orientable surfaces of genus $g'>g\ge 1$, and $f:F\to F$ be any pseudo-Anosov map. Then we can "extend" $f$ to be a pseudo-Anosov map $f':F'\to F'$ so that there is a fiber preserving degree one map $M(F',f')\to…

We study diffeomorphisms of compact, oriented surfaces, developing methods of distinguishing those which have positive factorizations into Dehn twists from those which satisfy the weaker condition of right veering. We use these to construct…

We construct analytic pseudo-rotations on the sphere and the disk with specific properties. We obtain analytic pseudo-rotations which are ergodic. Then, in opposition to ergodicity, we construct analytic pseudo-rotations which exhibit a…

We prove that generic elements of braid groups are pseudo-Anosov, in the following sense: in the Cayley graph of the braid group with n $\ge$ 3 strands, with respect to Garside's generating set, we prove that the proportion of pseudo-Anosov…

Despite the invertible setting, Anosov endomorphisms may have infinitely many unstable directions. Here we prove, under transitivity assumption, that an Anosov endomorphism on a closed manifold $M,$ is either special (that is, every $x \in…

In this paper we introduce a new methodology for smooth rigidity of Anosov diffeomorphisms based on "matching functions." The main observation is that under certain bunching assumptions on the diffeomorphism the periodic cycle functionals…

In this paper, we show that some spectral properties of Anosov diffeomorphisms can be obtained by semi-classical analysis. In particular the Ruelle resonances which are eigenvalues of the Ruelle transfer operator acting in suitable…

The fine curve graph was introduced as a geometric tool to study homeomorphisms of surfaces. In this paper we study the Gromov boundary of this space and the local topology near points associated with certain foliations and laminations. We…

We prove a local trace formula for Anosov flows. It relates Pollicott--Ruelle resonances to the periods of closed orbits. As an application, we show that the counting function for resonances in a sufficiently wide strip cannot have a…