The cohomological equation for partially hyperbolic diffeomorphisms

2008

58 citations recorded by the source corpus.

We establish a theory for the existence and regularity of solutions to the cohomological equation over an accessible, partially hyperbolic diffeomorphism. As a by-product of our techniques, we show that for $r>1$, any $C^r$ homogeneous, locally compact submanifold of a $C^r$ manifold is in fact a $C^r$ submanifold.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/36eeb246cbcf9ef20782ce851bc8a5e6a127e647

Citations in the corpus

• Absolute continuity, Lyapunov exponents and rigidity I : geodesic flows (2011, unknown): “A result of Repovš, Skopenkov and Ščepin [43] implies that graph(1v) is a C submanifold of Ev ×R (see also [53]).”
• Accessibility (2018, unknown): “Furthermore, accessibility enables the generalization of periodic obstructions to solving the cohomological equation and Livsic regularity problems for partially hyperbolic diffeomorphisms [Wil13].”