In this survey we describe how the so-called Dold congruence arises in topology, and how it relates to periodic point counting in dynamical systems.

Evolution of sound in a medium whose properties irreversibly vary in the course of wave propagation, is studied. For example, a gas that is a particular case of a Newtonian fluid is considered. Hysteresis curves, pictorial representations of irreversible attenuation of the sound energy, in the plane of thermodynamic states are plotted. The irreversible losses in internal energy are proportional to the total attenuation and depend...

Let S^2 be a two-dimensional sphere. We consider two types of its foliations with one singularity and maps f:S^2→S^2 preserving these foliations, more and less regular. We prove that in both cases f has at least |deg(f)| fixed points, where deg(f) is a topological degree of f. In particular, the lower growth rate of the number of fixed points of the iterations of f is at least log|deg(f)|. This confirms the Shub’s conjecture in...

The vortex ow which follows intense sound propagating in a bubbly liquid, is considered. The reasons for acoustic streaming are both nonlinearity and dispersion. That makes streaming especial as compared with that in a Newtonian uid. Conclusions concern the vortex ow induced in a half-space by initially harmonic or impulse Gaussian beam. The vortex ow recalls a turbulent ow with increasing in time number of small-scale vortices...

A thermodynamic relation between perturbations of pressure and mass density in the magnetohydrodynamic flow is theoretically studied. Planar magnetohydrodynamic perturbations with the wave vector, which forms a constant angle with the equilibrium magnetic field, are under study. The theory considers thermal conduction of a plasma and the deviation from adiabaticity of a flow due to some kind of heating–cooling function. It also...