相关论文: Anosov diffeomorphisms on infra-nilmanifolds assoc…

We show that time-one maps of transitive Anosov flows of compact manifolds are accumulated by diffeomorphisms robustly satisfying the following dichotomy: either all of the measures of maximal entropy are non-hyperbolic, or there are…

We show that most homogeneous Anosov actions of higher rank Abelian groups are locally smoothly rigid (up to an automorphism). This result is the main part in the proof of local smooth rigidity for two very different types of algebraic…

We prove several rigidity properties for random quotients of mapping class groups of surfaces, namely whose kernel is normally generated by the n-th steps of finitely many independent random walks. Firstly, we generalise a celebrated…

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…

In this paper, we study Homeo$^1(S)$, the group of homeomorphisms of a surface that preserve the set of one-dimensional $C^1$ submanifolds of that surface. The group Homeo$^1(S)$ belongs to a family of similarly defined groups Homeo$^k(S)$…

Let M be a closed orientable irreducible 3-manifold, and let f be a diffeomorphism over M. We call an embedded 2-torus T an Anosov torus if it is invariant and the induced action of f over \pi_1(T) is hyperbolic. We prove that only few…

We know from previous work with Italiano and Migliorini that there exists some hyperbolic 5-manifold that fibers over the circle. Here we build one example where the monodromy is a "pseudo-Anosov homeomorphism" of the 4-dimensional fiber,…

Weprovethattheasymptoticsofergodicintegralsalonganinvariant foliation of a toral Anosov diffeomorphism, or of a pseudo-Anosov diffeomorphism on a compact orientable surface of higher genus, are determined (up to a logarithmic error) by the…

We consider the hyperelliptic handlebody group on a closed surface of genus $g$. This is the subgroup of the mapping class group on a closed surface of genus $g$ consisting of isotopy classes of homeomorphisms on the surface that commute…

We present a way of constructing and deforming diffeomorphisms of manifolds endowed with a Lie group action. This is applied to the study of exotic diffeomorphisms and involutions of spheres and to the equivariant homotopy of Lie groups.

We study the topology of orbits of dynamical systems defined by finite-dimensional representations of nilpotent Lie groups. Thus, the following dichotomy is established: either the interior of the set of regular points is dense in the…

We exhibit Anosov subgroups of $\mathsf{SL}_d(\mathbb{R})$ that do not embed discretely in any rank-$1$ simple Lie group of noncompact type, or indeed, in any finite product of such Lie groups. These subgroups are isomorphic to free…

We show that partially hyperbolic diffeomorphisms of $d$-dimensional tori isotopic to an Anosov diffeomorphism, where the isotopy is contained in the set of partially hyperbolic diffeomorphisms, are dynamically coherent. Moreover, we show a…

The invariant measured foliations of a pseudo-Anosov homeomorphism induce a natural (singular) Sol structure on mapping tori of surfaces with pseudo-Anosov monodromy. We show that when the pseudo-Anosov $\phi:S\rightarrow S$ has orientable…

The goal of this paper is to explore the relationship between the geometric properties of an Anosov flow on a closed manifold $M$ and the analytic properties of its infinitesimal generator $X$ as a linear operator on the space of smooth…

The theorem by Lewandowski et al. stating uniqueness of a diffeomorphism invariant state on an algebra of quantum observables for background independent theories of connections is based on some technical assumptions imposed on the algebra…

Let $M$ be a flat manifold. We say that $M$ has $R_\infty$ property if the Reidemeister number $R(f) = \infty$ for every homeomorphism $f \colon M \to M.$ In this paper, we investigate a relation between the holonomy representation $\rho$…

Given a locally constant linear cocycle over a subshift of finite type, we show that the existence of a uniform gap between the i-th and (i+1)-th Lyapunov exponents for all invariant measures implies the existence of a dominated splitting…

In this work we study the class of mostly expanding partially hyperbolic diffeomorphisms. We prove that such class is $C^r$-open, $r>1$, among the partially hyperbolic diffeomorphisms (in the narrow sense) and we prove that the mostly…

We develop a homotopy theory of directed graphs based on cubical homotopy groups, also referred to as A-groups or reduced GLMY homotopy groups. Localizing the category of directed graphs at morphisms that induce isomorphisms on these groups…