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Mathematics > Dynamical Systems

arXiv:0708.1017 (math)
[Submitted on 7 Aug 2007 (v1), last revised 19 Jun 2008 (this version, v4)]

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

Authors: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.
Comments: 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
Subjects: Dynamical Systems (math.DS)
Cite as: arXiv:0708.1017 [math.DS]
  (or arXiv:0708.1017v4 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.0708.1017

Submission history

From: Dan Jane [view email]
[v1] Tue, 7 Aug 2007 23:00:13 UTC (16 KB)
[v2] Thu, 27 Sep 2007 10:57:02 UTC (17 KB)
[v3] Thu, 29 Nov 2007 13:54:12 UTC (17 KB)
[v4] Thu, 19 Jun 2008 21:19:13 UTC (18 KB)
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