Smoothness of horocycle foliations

Hh Older Regularity of Horocycle Foliations

On the Smoothness of Levi-foliations

D.E . BARRETT AND J . E . FORNAESS We study the regularity of the induced foliation of a Levi-flat hypersurface in C'° , showing that the foliation is as many times continuously differentiable as the hypersurface itself. The key step in the proof given here is the construction of a certain family of approximate plurisubharmonic defining functions for the hypersurface in question .

Normal forms on contracting foliations: smoothness and homogeneous structure

In this paper we consider a diffeomorphism f of a compact manifold M which contracts an invariant foliation W with smooth leaves. If the differential of f on TW has narrow band spectrum, there exist coordinates Hx : Wx → TxW in which f |W has polynomial form. We present a modified approach that allows us to construct mapsHx that depend smoothly on x along the leaves of W . Moreover, we show tha...

Quotients of Horocycle

In this paper we investigate the long term asymptotic properties of what might be called the induced horocycle ow on a compact quotient of the Poincar e upper half plane. We nd that this \\ow" exhibits chaotic properties in the sense that, in the long term, the area of the intersection of an open ball propagated forward by the \\ow," with the original ball, tends to what would be expected if th...

Ergodicity of the Horocycle Flow

We prove that ergodicity of the horocycle ow on a surface of constant negative curvature is equivalent to ergodicity of the associated boundary action. As a corollary we obtain ergodicity of the horocycle ow on several large classes of covering surfaces. There are two natural \geometric ows" on (the unitary tangent bundle of) an arbitrary surface of constant negative curvature: the geodesic and...