Related papers: Impulsive Lorenz semiflows: Physical measures, sta…
We define the empiric stochastic stability of an invariant measure in the finite-time scenario, the classical definition of stochastic stability. We prove that an invariant measure of a continuous system is empirically stochastically stable…
This paper studies the asymptotic behaviour of the solution of a differential equation perturbed by a fast flow preserving an infinite measure. This question is related with limit theorems for non-stationary Birkhoff integrals. We…
A new concept of semi-compressible fluids is introduced for slightly compressible visco-elastic fluids (typically rather liquids than gasses) where mass density variations are negligible in some sense, while being directly controlled by…
In this thesis we investigate the instabilities of superfluids at finite superflow by means of a hydrodynamical approach. We find that at a finite value of the background superfluid velocity a hydrodynamic collective mode crosses to the…
The stability of shear flows of electrically conducting fluids, with respect to finite amplitude three-dimensional localized disturbances is considered. The time evolution of the fluid impulse integral, characterizing such disturbances, for…
We study the notion of stochastic stability with respect to diffusive perturbations for flows with smooth invariant measures. We investigate the question fully for non-singular flows on the circle. We also show that volume-preserving flows…
This paper is a review on recently found connection between geodesically equivalent metrics and integrable geodesic flows. Suppose two different metrics on one manifold have the same geodesics. We show that then the geodesic flows of these…
Pressure measures the complexity of a dynamical system concerning a continuous observation function. A dynamical system is called to admit the intermediate pressure property if for any observation function, the measure theoretical pressures…
Enstrophy is an averaged measure of fluid vorticity. This quantity is particularly important in {\em rotating} geophysical flows. We investigate the dynamical evolution of enstrophy for large-scale quasi-geostrophic flows under random wind…
The Doppler effect, the shift in the frequency of sound due to motion, is present in both classical gases and quantum superfluids. Here, we perform an in-situ, minimally destructive measurement, of the persistent current in a ring-shaped,…
The aim of this note is to point out some observations concerning modified power entropy of $\Z$- and $\N$-actions. First, we provide an elementary example showing that this quantity is sensitive to transient dynamics, and therefore does…
Impulsive semiflows modeled by continuous flows and continuous impulsive functions, defined over an impulsive region, are piecewise continuous semiflows with piecewise smooth trajectories. In this paper we contribute to the topological…
We detect, by using symplectic topology, invariant measures with large rotation vectors for a class of Hamiltonian flows.
In this paper, we consider turbulence from a geometric perspective based on the vorticity equations for incompressible viscous fluid flows. We derive several quantitative statements about the statistics of turbulent flows. In particular we…
A convenient measure of a map or flow's chaotic action is the topological entropy. In many cases, the entropy has a homological origin: it is forced by the topology of the space. For example, in simple toral maps, the topological entropy is…
We consider equations describing a barotropic inviscid flow in a channel with topography effects and beta-plane approximation of Coriolis force, in which a large-scale mean flow interacts with smaller scales. Gibbsian measures associated to…
Various notions of "zooming in" on measures exist in the literature and the scenery flow is one of them. It is of interest to describe the joint asymptotics of the scenery flows generated by a measure and the measure transported by a local…
An invariant measure for a flow is, of course, an invariant measure for any of its time-t maps. But the converse is far from being true. Hence, one may naturally ask: What is the obstruction for an invariant measure for the time-one map to…
We prove local limit theorems for a cocycle over a semiflow by establishing topological, mixing properties of the associated skew product semiflow. We also establish conditional rational weak mixing of certain skew product semiflows and…
Lagrangian properties obtained from a Particle Tracking Velocimetry experiment in a turbulent flow at intermediate Reynolds number are presented. Accurate sampling of particle trajectories is essential in order to obtain the Lagrangian…