| On the injectivity of the X-ray transform for Anosov thermostats (2007) | |||||||||
Abstract | |||||||||
| 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.. Comment: Revised version more explicitly outlines an open problem in the introduction, and corrects a typo in the Lie brackets of page 4. An appendix rewritten for clarity in the second revision. Final version as accepted by DCDS-A | |||||||||
Publication details | |||||||||
| |||||||||