Related papers: Cherry flow: physical measures and perturbation th…
We investigate the invariant probability measures for Cherry flows, i.e. flows on the two-torus which have a saddle, a source, and no other fixed points, closed orbits or homoclinic orbits. In the case when the saddle is dissipative or…
Studies of the physical measures for Cherry flows were initiated by R. Saghin and E. Vargas in "Invariant measures for Cherry flows". While the non-positive divergence case was resolved, the positive divergence one still lacked the complete…
We provide an example of Cherry flow (i.e. smooth flow on the $2$-dimensional torus with a sink and a saddle) having quasi-minimal set which is an attractor. The first return map for such a flow, constructed also in the paper, is a smooth…
We describe all possible topological structures of Morse flows and typical gradient saddle-nod bifurcation of flows on the 2-dimensional torus with a hole in the case that the number of singular point of flows is at most six. To describe…
In this paper we study the large time asymptotics of the flow of a dynamical system $X'=b(X)$ posed in the $d$-dimensional torus. Rather than using the classical unique ergodicity condition which is not fulfilled if $b$ vanishes at…
We describe all possible topological structures of typical one-parameter bifurcations of gradient flows on the 2-sphere with holes in the case that the number of singular point of flows is at most six. To describe structures, we separatrix…
We consider barotropic instability of shear flows for incompressible fluids with Coriolis effects. For a class of shear flows, we develop a new method to find the sharp stability conditions. We study the flow with Sinus profile in details…
An open question in the study of dilation surfaces is to determine the typical dynamical behavior of the directional flow on a fixed dilation surface. We show that on any one-holed dilation torus, in all but a measure zero Cantor set of…
Circle maps frequently arise in mathematical models of physical or biological systems. Motivated by Cherry flows and `threshold' systems such as integrate and fire neuronal models, models of cardiac arrhythmias, and models of sleep/wake…
In this paper we consider non-singular Morse-Smale flows on closed orientable 3-manifolds, under the assumption that among the periodic orbits of the flow there is only one saddle orbit and it is twisted. It is found that any manifold…
The transport of slightly deformable chiral objects in a uniform shear flow is investigated. Depending on the equilibrium configuration one finds up to four different asymptotic states that can be distinguished by a lateral drift velocity…
This paper investigates the properties of trajectories in harmonic oscillator systems equipped with a point, absolutely continuous, or singular measure. As demonstrated in [30], infinite-dimensional linear flows of countable oscillator…
The possibility that the magnetic shear-flow instability (MRI, Balbus-Hawley instability) might give rise to turbulence in a cylindric Couette flow is investigated through numerical simulations. The study is linear and the fluid flow is…
In the present paper, non-singular Morse-Smale flows on closed orientable 3-manifolds under the assumption that among the periodic orbits of the flow there is only one saddle one and it is twisted are considered. An exhaustive description…
We describe all possible topological structures of typical one-parameter bifurcations of gradient flows on the 2-sphere with holes in the case that the number of singular point of flows is at most six. To describe structures, we separatrix…
We propose a simple method to identify unstable parameter regions in general inviscid unidirectional shear flow stability problems. The theory is applicable to a wide range of basic flows, including those that are non-monotonic. We…
The Ricci flow on the 2-sphere with marked points is shown to converge in all three stable, semi-stable, and unstable cases. In the stable case, the flow was known to converge without any reparametrization, and a new proof of this fact is…
In this paper, the physics of flow instability and turbulent transition in shear flows is studied by analyzing the energy variation of fluid particles under the interaction of base flow with a disturbance. For the first time, a model…
Flow instability and turbulent transition can be well explained using a new proposed theory--Energy gradient theory [1]. In this theory, the stability of a flow depends on the relative magnitude of energy gradient in streamwise direction…
The subject of this work is the instability mechanism of simple shear flows, like Hagen-Poiseuille pipe flow, which is a long-standing problem in fluid mechanics [1,2]. A possible analogy with phenomenological theory of ideal plasticity in…