Related papers: Upper large deviations bound for singular-hyperbol…

We show that a sectional-hyperbolic attracting set for a H\"older-$C^1$ vector field admits finitely many physical/SRB measures whose ergodic basins cover Lebesgue almost all points of the basin of topological attraction. In addition, these…

Over the last 10 years or so, advanced statistical properties, including exponential decay of correlations, have been established for certain classes of singular hyperbolic flows in three dimensions. The results apply in particular to the…

We study the asymptotic properties of the trajectories of a discrete-time random dynamical system in an infinite-dimensional Hilbert space. Under some natural assumptions on the model, we establish a multiplica-tive ergodic theorem with an…

We introduce a new version of expansiveness for flows. Let $M$ be a compact Riemannian manifold without boundary and $X$ be a $C^1$ vector field on $M$ that generates a flow $\varphi_t$ on $M$. We call $X$ {\it rescaling expansive} on a…

We study suspension flows defined over sub-shifts of finite type with continuous roof functions. We prove the existence of suspension flows with uncountably many ergodic measures of maximal entropy. More generally, we prove that any…

We obtain $q$-Wasserstein convergence rates in the invariance principle for nonuniformly hyperbolic flows, where $q\ge1$ depends on the degree of nonuniformity. Utilizing a martingale-coboundary decomposition for nonuniformly expanding…

We investigate superdiffusion for stochastic processes generated by nonuniformly hyperbolic system models, in terms of the convergence of rescaled distributions to the normal distribution following the abnormal central limit theorem, which…

In this paper we establish the existence and uniqueness of global solutions (in time), as well as the existence, regularity and stability (upper semicontinuity) of the attractor for the semigroup generated by the solutions of a…

We show the existence and uniqueness of the maximal entropy probability measure for partially hyperbolic diffeomorphisms which are semi-conjugate to nonuniformly expanding maps. Using the theory of projective metric on cones we then prove…

For a surface diffeomorphism, a compact invariant locally maximal set $W$ and some subset $A\subset W$ we study the $A$-exceptional set, that is, the set of points whose orbits do not accumulate at $A$. We show that if the Hausdorff…

In this paper, concerning SDEs with H\"older continuous drifts, which are merely dissipative at infinity, and SDEs with piecewise continuous drifts, we investigate the strong law of large numbers and the central limit theorem for underlying…

Let f be a self-map of a compact manifold M, admitting an global SRB measure \mu. For a continuous test function \phi on M and a constant \alpha>0, consider the set of the initial points for which the Birkhoff time averages of the function…

We prove a sharp large deviation principle concerning intervals shrinking with sub-exponential speed for certain models involving the Poincar\'e map related to a Markov family for an Axiom A flow restricted to a basic set $\Lambda$…

For diffeomorphisms or for non-singular flows, there are many results relating properties persistent under C1 perturbations and global structures for the dynamics ( such as hyperbolicity, partial hyperbolicity, dominated splitting).…

For a certain parametrized family of maps on the circle, with critical points and logarithmic singularities where derivatives blow up to infinity, a positive measure set of parameters was constructed in [19], corresponding to maps which…

A {\em singular hyperbolic set} is a partially hyperbolic set with singularities (all hyperbolic) and volume expanding central direction \cite{MPP1}. We study connected, singular-hyperbolic, attracting sets with dense closed orbits {\em and…

Hyperbolic structures are obtained by tiling a hyperbolic surface with negative Gaussian curvature. These structures generally exhibit two percolation transitions: a system-wide connection can be established at a certain occupation…

We study the second-order asymptotics around the superdiffusive strong law~\cite{MMW} of a multidimensional driftless diffusion with oblique reflection from the boundary in a generalised parabolic domain. In the unbounded direction we prove…

We present a singular perturbation theory applicable to systems with hybrid boundary layer systems and hybrid reduced systems {with} jumps from the boundary layer manifold. First, we prove practical attractivity of an adequate attractor set…

Using an approach due to Bowen, Franco showed that continuous expansive flows with specification have unique equilibrium states for potentials with the Bowen property. We show that this conclusion remains true using weaker non-uniform…