Related papers: Smooth orbit equivalence rigidity for dissipative …

Let $M$ be a connected compact orientable surface, $f:M\to \mathbb{R}$ be a Morse function, and $h:M\to M$ be a diffeomorphism which preserves $f$ in the sense that $f\circ h = f$. We will show that if $h$ leaves invariant each regular…

For warped products with harmonic curvature, nonconstant warping functions $\phi$, and compact two-dimensional bases $(M,h)$, we establish a dichotomy: either the Gaussian curvature $K$ of the metric $g=\phi^{-2}h$ is constant and negative,…

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 ${\bf e}$.…

Let $M$ be a closed oriented surface and let $\Omega$ be a non-exact 2-form. Suppose that the magnetic flow $\phi$ of the pair $(g,\Omega)$ is Anosov. We show that the longitudinal KAM-cocycle of $\phi$ is a coboundary if and only the…

We give conditions for when continuous orbit equivalence of one-sided shift spaces implies flow equivalence of the associated two-sided shift spaces. Using groupoid techniques, we prove that this is always the case for shifts of finite…

In this paper, we prove that if the geodesic flow of a complete manifold without conjugate points with sectional curvatures bounded below by $-c^2$ is of Anosov type, then the constant of contraction of the flow is $\geq e^{-c}$. Moreover,…

Let $M$ be a closed 3-manifold admitting a finite cover of index n along the fibers over the unit tangent bundle of a closed surface. We prove that if n is odd, there is only one Anosov flow on M up to orbital equivalence, and if n is even,…

Let $M$ be a closed surface and let $\{g_s \ | \ s \in (-\epsilon, \epsilon)\}$ be a smooth one-parameter family of Riemannian metrics on $M$. Also let $\{\kappa_s : M \rightarrow \mathbb{R} \ | \ s \in (-\epsilon, \epsilon)\}$ be a smooth…

We consider the Navier--Stokes equations for compressible heat-conducting ideal polytropic gases in a bounded annular domain when the viscosity and thermal conductivity coefficients are general smooth functions of temperature. A…

By a gradient-like flow on a closed orientable surface $M$, we mean a closed 1-form $\beta$ defined on $M$ punctured at a finite set of points (sources and sinks of $\beta$) such that there exists a Morse function $f$ on $M$, called an…

In this paper we show that the geodesic flow of a Finsler metric is Anosov if and only if there exists a $C^2$ open neighborhood of Finsler metrics all of whose closed geodesics are hyperbolic. For surfaces this result holds also for…

Two flows are topologically almost commensurable if, up to removing finitely many periodic orbits and taking finite coverings, they are topologically equivalent. We prove that all suspensions of automorphisms of the 2-dimensional torus and…

We show the flexibility of the metric entropy and obtain additional restrictions on the topological entropy of geodesic flow on closed surfaces of negative Euler characteristic with smooth non-positively curved Riemannian metrics with fixed…

Suppose we are given a compact Riemannian manifold (Q,g)with completely integrable geodesic flow. Let G be a compact connected Lie group acting freely on Q by isometries. The natural question arises: will the geodesic flow on Q/G equipped…

Let $M$ be a pinched negatively curved Riemannian orbifold, whose fundamental group has torsion of order $2$. Generalizing results of Sarnak and Erlandsson-Souto for constant curvature oriented surfaces, and with very different techniques,…

We prove here that given a proper isometric action $K\times M\to M$ on a complete Riemannian manifold $M$ then every continuous isometric flow on the orbit space $M/K$ is smooth, i.e., it is the projection of an $K$-equivariant smooth flow…

We present evidence indicating that Anosov systems can be endowed with a unique physically reasonable effective temperature. Results for the two paradigmatic Anosov systems (i.e., the cat map and the geodesic flow on a surface of constant…

The irrotational vortex geometry carachter of torsion loops is displayed by showing that torsion loops and nonradial flow acoustic metrics are conformally equivalent in $(1+1)$ dimensions while radial flow acoustic spacetime are conformally…

We study resonant differential forms at zero for transitive Anosov flows on $3$-manifolds. We pay particular attention to the dissipative case, that is, Anosov flows that do not preserve an absolutely continuous measure. Such flows have two…

In this work we show that the set of Kupka-Smale Gaussian thermostats on a compact manifold is generic. A Gaussian thermostat is Kupka-Smale if the closed orbits are hyperbolic and the heteroclinic intersection are transversal. We also show…