On the cohomological equation of magnetic flows (2008)
Dairbekov, Nurlan S., Paternain, Gabriel P.
We consider a magnetic flow without conjugate points on a closed manifold $M$ with generating vector field $\G$. Let $h\in C^{\infty}(M)$ and let $\theta$ be a smooth 1-form on $M$. We show that the...
Entropy production in thermostats II (2006)
Dairbekov, Nurlan S., Paternain, Gabriel P.
We show that an arbitrary Anosov Gaussian thermostat close to equilibrium has positive entropy poduction unless the external field $E$ has a global potential. The configuration space is allowed to...
Rigidity properties of Anosov optical hypersurfaces (2005)
Dairbekov, Nurlan S., Paternain, Gabriel P.
We consider an optical hypersurface $\Sigma$ in the cotangent bundle $\tau:T^*M\to M$ of a closed manifold $M$ endowed with a twisted symplectic structure. We show that if the characteristic...
Lengths and volumes in Riemannian manifolds (2004)
Croke, Christopher B., Nurlan S. Dairbekov
We consider the question of when an inequality between lengths of corresponding geodesics implies a corresponding inequality between volumes. We prove this in a number of cases for compact manifolds...