Hypercyclic operators on countably dimensional spaces

According to Grivaux, the group $GL(X)$ of invertible linear operators on a separable infinite dimensional Banach space $X$ acts transitively on the set $\Sigma(X)$ of countable dense linearly independent subsets of $X$. As a consequence, each $A\in \Sigma(X)$ is an orbit of a hypercyclic operator on $X$. Furthermore, every countably dimensional normed space supports a hypercyclic operator. We show that for a separable infinite dimensional Fr\'echet space $X$, $GL(X)$ acts transitively on $\Sigma(X)$ if and only if $X$ possesses a continuous norm. We also prove that every countably dimensional metrizable locally convex space supports a hypercyclic operator

Excitation of acoustic waves by vortices in the quiet Sun

Five-minutes oscillations is one of the basic properties of solar convection. Observations show mixture of a large number of acoustic wave fronts propagating from their sources. We investigate the process of acoustic waves excitation from the point of view of individual events, by using realistic 3D radiative hydrodynamic simulation of the quiet Sun. The results show that the excitation events are related to dynamics vortex tubes (or swirls) in the intergranular lanes. These whirlpool-like flows are characterized by very strong horizontal velocities (7 - 11 km/s) and downflows (~ 7 km/s), and are accompanied by strong decreases of the temperature, density and pressure at the surface and in a ~ 0.5-1 Mm deep layer below the surface. High-speed whirlpool flows can attract and capture other vortices. According to our simulation results, the processes of the vortex interaction, such as vortex annihilation, can cause the excitation of acoustic waves.Comment: 10 pages, 5 figure, submitted to ApJ