Related papers: Anosov magnetic flows on surfaces

Magnetic geodesics describe the trajectory of a particle in a Riemannian manifold under the influence of an external magnetic field. In this article, we use the heat flow method to derive existence results for such curves. We first…

The purpose of this paper is to prove that, for every $n\in \mathbb N$, there exists a closed hyperbolic $3$-manifold $M$ which carries at least $n$ non-$\mathbb R$-covered Anosov flows, that are pairwise orbitally inequivalent. Due to a…

Quasigeodesic behavior of flow lines is a very useful property in the study of Anosov flows. Not every Anosov flow in dimension three is quasigeodesic. In fact up to orbit equivalence, the only previously known examples of quasigeodesic…

For each natural number n, we construct an example of a graph manifold supporting at least n different Anosov flows that are not orbit equivalent. Our construction is reminiscent of the Thurston-Handel construction: we cut a geodesic flow…

Bifoliated planes arise naturally in the study of Anosov flows on $3$-manifolds. To any Anosov flow on a $3$-manifold $M$, one can associate a bifoliated plane equipped with an action of the fundamental group of $M$ which encodes the…

We consider a billiard in the sphere S^2 with circular obstacles, and give a sufficient condition for its flow to be uniformly hyperbolic. We show that the billiard flow in this case is approximated by an Anosov geodesic flow on a surface…

We give some simple conditions under which a group acting on a bifoliated plane comes from the induced action of a pseudo-Anosov flow on its orbit space. An application of the strategy is a less technical proof of a result of Barbot that…

For Anosov flows preserving a smooth measure on a closed manifold $\mathcal{M}$, we define a natural self-adjoint operator $\Pi$ which maps into the space of invariant distributions in $\cap_{u<0} H^{u}(\mathcal{M})$ and whose kernel is…

The problem of reconstruction of a flow of conducting incompressible fluid generating a given magnetic mode is considered. We use the magnetic induction equation to derive ordinary differential equations along the magnetic field lines,…

Several recent experimental studies have confirmed the possibility of switching the magnetization direction in the small magnetic domains by pumping large spin-polarized currents through them. On the basis of equations proposed by…

Using the factorization method, a method pioneered by Eskin and Mirzakhani in their groundbreaking work about measure classification over the moduli space of translation surfaces, we show that generalized $u$-Gibbs states over…

Given an Anosov flow on a closed 3-manifold, we are interested in the problem of whether or not making non-trivial Fried surgeries along a finite set of periodic orbits can produce a flow equivalent to itself. We show that for some…

Let $M$ be a closed oriented surface endowed with a Riemannian metric $g$. We consider the flow $\phi$ determined by the motion of a particle under the influence of a magnetic field $\Omega$ and a thermostat with external field ${\bf e}$.…

We analyze a class of physical properties, forming the content of the so-called von Zeipel theorem, which characterizes stationary, axisymmetric, non-selfgravitating perfect fluids in circular motion in the gravitational field of a compact…

We study minimal transverse foliations which are $R$-covered. If in addition the dimension of the ambient manifold is $3$, and the foliations are Anosov foliations we give necessary and sufficient conditions for the intersected foliation to…

We study the behaviour of the Ricci Yang-Mills flow for U(1) bundles on surfaces. We show that existence for the flow reduces to a bound on the isoperimetric constant. In the presence of such a bound, we show that on $S^2$, if the bundle is…

We prove that in dimension 3, Anosov flows which are $\mathbb{R}$-covered and skewed are orbit equivalent to Reeb-Anosov flows. We characterize the existence of an invariant contact form or of a Birkhoff section with a given boundary, in…

We construct fully three-dimensional (3D) equilibria with pressure anisotropy and closed, nested toroidal magnetic surfaces that are strongly asymmetric in the toroidal direction by applying a sinusoidal perturbation to the axisymmetric…

A simplified model for the stationary, axisymmetric structure of magnetized winds with a polytropic equation of state is presented. The shape of the magnetic surfaces is assumed to be known (conical in this paper) within the fast…

For Anosov flows obtained by suspensions of Anosov diffeomorphisms on surfaces, we show the following type of rigidity result: if a topological conjugacy between them is differentiable at a point, then the conjugacy has a smooth extension…