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DCDS

We prove an inequality for Hölder continuous differential forms on
compact manifolds in which the integral of the form over the
boundary of a sufficiently small, smoothly immersed disk is bounded
by a certain multiplicative convex combination of the volume of the
disk and the area of its boundary. This inequality has natural
applications in dynamical systems, where Hölder continuity is
ubiquitous. We give two such applications. In the first one, we
prove a criterion for the existence of global cross sections to
Anosov flows in terms of their expansion-contraction rates. The
second application provides an analogous criterion for
non-accessibility of partially hyperbolic diffeomorphisms.

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