Hölder forms and integrability of invariant distributions

Details Hölder forms and integrability of invariant distributions Hölder forms and integrability of invariant distributions

2007-08-14

arxiv.org/abs/0708.1940v4

Mathematics

Dynamical Systems

The paper has been revised. To appear in Discrete and Continuous Dynamical Systems

Scientific paper

We prove an inequality for H\"older 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 H\"older 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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