Related papers: Ergodic theorems for laminations and foliations: r…
In this work we treat a famous topic in Ergodic Theory and Dynamical Systems: uniformly expanding maps. We relate regularity of expanding maps and conjugacies with Lyapunov exponents, metric and topological entropies for expanding maps of…
These lecture notes attempt to invite the reader towards the theory of singular foliations, both smooth and holomorphic. In addition to a systematic review of the foundations, and an attempt to put in order examples and several elementary…
We introduce a notion of stability for equilibrium measures in holomorphic families of endomorphisms of CP(k) and prove that it is equivalent to the stability of repelling cycles and equivalent to the existence of some measurable…
The aim of this paper is to develop a theory of finite transformation monoids and in particular to study primitive transformation monoids. We introduce the notion of orbitals and orbital digraphs for transformation monoids and prove a…
In this paper we study the thermodynamic formalism of strongly transitive endomorphisms $f$, focusing on the set all expanding measures. In case $f$ is a non-flat $C^{1+}$ map defined on a Riemannian manifold, these are invariant…
We study the stability of pullback foliations under morphisms and rational maps via Grothendieck's Drapeaux scheme. In the local setting, a foliated version of Schlessinger's Theorem on rigidity of conical singularities was achieved. We…
We prove a compactness theorem for embedded measured hyperbolic Riemann surface laminations in a compact almost complex manifold $(X, J)$. To prove compactness result, we show that there is a suitable topology on the space of measured…
We address the problem of existence and uniqueness (finite- ness) of ergodic equilibrium states for a natural class of partially hyperbolic dynamics homotopic to Anosov. We propose to study the disintegration of equilibrium states along…
We develop a variational theory of geodesics for the canonical variation of the metric of a totally geodesic foliation. As a consequence, we obtain comparison theorems for the horizontal and vertical Laplacians. In the case of Sasakian…
This paper studies ergodic properties of certain measures arising in the dynamics of holomorphic correspondences. These measures, in general, are not invariant in the classical sense of ergodic theory. We define a notion of ergodicity, and…
We show that for a taut foliation F with one-sided branching of an atoroidal 3-manifold M, one can construct a pair of genuine laminations with solid torus complementary regions which bind every leaf of F in a geodesic lamination. These…
A result for subadditive ergodic cocycles is proved that provides more delicate information than Kingman's subadditive ergodic theorem. As an application we deduce a multiplicative ergodic theorem generalizing an earlier result of…
We consider the action of $SL(2,\mathbb{R})$ on a vector bundle $\mathbf{H}$ preserving an ergodic probability measure $\nu$ on the base $X$. Under an irreducibility assumption on this action, we prove that if $\hat\nu$ is any lift of $\nu$…
Isoparametric submanifolds and hypersurfaces in space forms are geometric objects that have been studied since E. Cartan. Another important class of geometric objects is the orbits of a polar action on a Riemannian manifold,e.g., the orbits…
Consider a family of K3 surfaces over a hyperbolic curve (i.e. Riemann surface). Their second cohomology groups form a local system, and we show that its top Lyapunov exponent is a rational number. One proof uses the Kuga-Satake…
Consider a Brody hyperbolic foliation with non-degenerate singularities on a compact complex manifold. We show that the leafwise heat diffusions and the abstract heat diffusions coincide. In particular, this will imply that the abstract…
A singular foliation is called a singular Riemannian foliation (SRF) if every geodesic that is perpendicular to one leaf is perpendicular to every leaf it meets. A typical example is the partition of a complete Riemannian manifold into…
Motivated by representation theory and geometry, we introduce and develop an equivariant generalization of Ehrhart theory, the study of lattice points in dilations of lattice polytopes. We prove representation-theoretic analogues of…
In this paper we study topological aspects of the dynamics of the foliated horocycle flow on flat projective bundles over hyperbolic surfaces and we derive ergodic consequences. If $\rho : \Gamma \to {\rm PSL}(n+1,\mathbb{R})$ is a…
We consider the construction and classification of some new mathematical objects, called ergodic spatial stationary processes, on locally compact Abelian groups, which provide a natural and very general setting for studying diffraction and…