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arXiv · 0708.1017

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

Dan Jane·Gabriel P. Paternain
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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.

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Dan Jane, Gabriel P. Paternain. 2008-06-19. On the injectivity of the X-ray transform for Anosov thermostats. https://arxiv.org/abs/0708.1017

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