On the injectivity of the X-ray transform for Anosov thermostats

Details On the injectivity of the X-ray transform for Anosov thermostats On the injectivity of the X-ray transform for Anosov thermostats

2007-08-07

arxiv.org/abs/0708.1017v4

Mathematics

Dynamical Systems

Revised version more explicitly outlines an open problem in the introduction, and corrects a typo in the Lie brackets of page

Scientific paper

We consider Anosov thermostats on a closed surface and the X-ray transform on functions which are up to degree two in the velocities. We show that the subspace where the X-ray transform fails to be s-injective is finite dimensional. Furthermore, if the surface is negatively curved and the thermostat is pure Gaussian (i.e. no magnetic field is present), then the X-ray transform is s-injective.

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