Related papers: Cocycles over interval exchange transformations an…

Let $\pi$ be a non-degenerate permutation on at least $4$ symbols. We show that the set of uniquely ergodic interval exchange transformations with permutation $\pi$ is path-connected.

We prove that for almost every irreducible interval exchange transformation $T$ and for any vector $\omega$ in its associated central-stable space (with respect to the Kontsevich-Zorich cocycle) there exists a unique AIET, up to…

Our main is to study periodic orbits of linear and invariant flows on a real, connected Lie group. Since each linear flow $\varphi_t$ has a derivation associated $\mathcal{D}$, we show that the existence of periodic orbits of $\varphi_t$ is…

We study some classes of semi-linear differential equations including both well-posed and ill-posed cases that can generate cocycles (or cocycle correspondences with generating cocycles). Under exponential dichotomy condition with other…

In this paper we give a criterion for a special flow to be not isomorphic to its inverse which is a refine of a result in \cite{Fr-Ku-Le}. We apply this criterion to special flows $T^f$ built over ergodic interval exchange transformations…

We study ergodic averages for a class of pseudodifferential operators on the flat N-dimensional torus with respect to the Schr\"odinger evolution. The later can be consider a quantization of the geodesic flow on $\bT^N$. We prove that, up…

We study the horocycle flow on the stratum of translation surfaces $\mathcal{H}(2)$. We show that there is a sequence of horocycle ergodic measures, each supported on a periodic horocycle orbit, which weakly converges to an invariant, but…

For some full measure subset B of the set of iet's (i.e. interval exchange transformations) the following is satisfied: Let X be a $C^r$, $1\le r\le \infty$, vector field, with finitely many singularities, on a compact orientable surface M.…

Ten years ago A. Zorich discovered, by computer experiments on interval exchange transformations, some striking new power laws for the ergodic integrals of generic non-exact Hamiltonian flows on higher genus surfaces. In Zorich's later work…

We show that ergodic flows in noncommutative fully symmetric spaces (associated with a semifinite von Neumann algebra) generated by continuous semigroups of positive Dunford-Schwartz operators and modulated by bounded Besicovitch almost…

I argue that certain bosonic insulator-superfluid phase transitions as an interaction constant varies are driven by emergent geometric properties of insulating states. The {\em renormalized} chemical potential and distribution of disordered…

We propose a general framework for constructing and describing infinite type flat surfaces of finite area. Using this method, we characterize the range of dynamical behaviors possible for the vertical translation flows on such flat…

We prove that almost every interval exchange transformation, with an associated translation surface of genus $g\geq 2$, can be non-trivially and isometrically embedded in a family of piecewise isometries. In particular this proves the…

In this article, we consider skew product extensions over symmetric interval exchange transformations with respect to the cocycle $f(x)=\chi_{(0,1/2)}-\chi_{(1/2,1)}$. More precisely, we prove that for almost every interval exchange…

We study the centraliser of locally compact group extensions of ergodic probability preserving transformations. New methods establishing ergodicity of group extensions are introduced, and new examples of squashable and non-coalescent group…

A translation surface on (S, \Sigma) gives rise to two transverse measured foliations \FF, \GG on S with singularities in \Sigma, and by integration, to a pair of cohomology classes [\FF], \, [\GG] \in H^1(S, \Sigma; \R). Given a measured…

We classify the periodic Hamiltonian flows on compact four dimensional symplectic manifolds up to isomorphism of Hamiltonian S^1 spaces. Additionally, we show that all these spaces are Kaehler, that every such space is obtained from a…

We show that generic infinite group extensions of geodesic flows on square tiled translation surfaces are ergodic in almost every direction, subject to certain natural constraints. Recently K. Fr\c{a}czek and C. Ulcigrai have shown that…

We prove that for a broad class of exact symplectic manifolds including ${\mathbb R}^{2m}$ the Hamiltonian flow on a regular compact energy level of an autonomous Hamiltonian cannot be uniquely ergodic. This is a consequence of the…

For Hamiltonian flows we establish the existence of periodic orbits on a sequence of level sets approaching a Bott-nondegenerate symplectic extremum of the Hamiltonian. As a consequence, we show that a charge on a compact manifold with a…