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

2007/08/07 by Dan Jane, Gabriel P. Paternain, Jane, Dan +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Statistical Mechanics and Entropy #Topological and Geometric Data Analysis #advanced mathematical theories #math.DS

paper · pdf · doi:10.48550/arxiv.0708.1017

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

openalex publication_date 2007/08/07 · arxiv created 2008/06/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Guillarmou's Normal Operator for Magnetic and Thermostat Flows

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