Related papers: Ergodic properties of equilibrium measures for smo…

The common assertion that the Ricci flows of Einstein spaces with cosmological constant can be modelled by certain classes of nonholonomic frame, metric and linear connection deformations resulting in nonhomogeneous Einstein spaces is…

We prove that in the isotopy class of any volume preserving partially hyperbolic diffeomorphism in a $3$-dimensional manifold, there is a non-partially hyperbolic stably ergodic diffeomorphism. In particular, we provide new examples of…

The main result of the paper is classification of free multidimensional Borel flows up to Lebesgue Orbit Equivalence, by which we understand an orbit equivalence that preserves the Lebesgue measure on each orbit. Two non smooth Euclidean…

We consider smooth area-preserving flows (also known as locally Hamiltonian flows) on surfaces of genus $g\geq 1$ and study ergodic integrals of smooth observables along the flow trajectories. We show that these integrals display a…

Quantum ergodicity asserts that almost all infinite sequences of eigenstates of a quantized ergodic system are equidistributed in the phase space. On the other hand, there are might exist exceptional sequences which converge to different…

We construct non-vanishing steady solutions to the Euler equations (for some metric) with analytic Bernoulli function in each three-manifold where they can exist: graph manifolds. Using the theory of integrable systems, any admissible…

We develop different synthetic notions of Ricci flow in the setting of time-dependent metric measure spaces based on ideas from optimal transport. They are formulated in terms of dynamic convexity and local concavity of the entropy along…

In this paper we study the ergodic theory of the geodesic flow on negatively curved geometrically finite manifolds. We prove that the measure theoretic entropy is upper semicontinuous when there is no loss of mass. In case we are losing…

An example of a real-analytic metric on a compact manifold whose geodesic flow is Liouville integrable by $C^\infty$ functions and has positive topological entropy is constructed.

This work aims to investigate the well-posedness and the existence of ergodic invariant measures for a class of third grade fluid equations in bounded domain $D\subset\mathbb{R}^d,d=2,3,$ in the presence of a multiplicative noise. First, we…

Under the assumption of a natural subadditive potential, the so called cylinder function, working on the symbol space we prove the existence of the ergodic invariant probability measure satisfying the equilibrium state. As an application we…

We examine high energy eigenfunctions for the Dirichlet Laplacian on domains where the billiard flow exhibits mixed dynamical behavior. (More generally, we consider semiclassical Schrodinger operators with mixed assumptions on the…

In this survey we recall basic notions of disintegration of measures and entropy along unstable laminations. We review some roles of unstable entropy in smooth ergodic theory including the so-called invariance principle, Margulis…

We prove that for a compact 3-manifold M with boundary admitting an ideal triangulation T with valence at least 10 at all edges, there exists a unique complete hyperbolic metric with totally geodesic boundary, so that T is isotopic to a…

We employ the ergodic theoretic machinery of scenery flows to address classical geometric measure theoretic problems on Euclidean spaces. Our main results include a sharp version of the conical density theorem, which we show to be closely…

We combine the two classical topological concepts, time-preserving topological factors and synchronizing time-changes of a continuous flow, and explore some of their thermodynamic consequences. Particular focus is put on equilibrium states…

In this article we consider the ergodic optimization for hyperbolic flows and Lorenz attractors with respect to both continuous and Holder continuous observables. In the context of hyperbolic flows we prove that a Baire generic subset of…

Let $(X,\mu)$ be a standard probability space. An automorphism $T$ of $(X,\mu)$ has the weak Pinsker property if for every $\varepsilon > 0$ it has a splitting into a direct product of a Bernoulli shift and an automorphism of entropy less…

We prove that a singular-hyperbolic attractor of a 3-dimensional flow is chaotic, in two strong different senses. Firstly, the flow is expansive: if two points remain close for all times, possibly with time reparametrization, then their…

Ergodic optimization aims to describe dynamically invariant probability measures that maximize the integral of a given function. For a wide class of intrinsically ergodic subshifts over a finite alphabet, we show that the space of…