Rigid reparametrizations and cohomology for horocycle flows
In a series of earlier papers the author proved various ``rigidity'' properties of the classical horocycle flow, namely the actions of the one-parameter subgroup \(\{\begin{pmatrix} 1&t \\ 0&1 \end{pmatrix}:\) \(t\in {\mathbb{R}}\}\) on homogeneous spaces of \(SL(2,{\mathbb{R}})\) with finite invariant volume, and other flows arising from them by time changes. The term rigidity refers to there being only canonical algebraic isomorphisms, factor relations, etc., between them. The present paper is a continuation of that work. It is shown that for flows obtained from horocycle flows by \(C^ 1\)-time changes all the ergodic joinings as well as their factors are algebraic. Also, nontrivial joining of two such flows is related to a certain cohomological relation between the time changes.
scientific article; zbMATH DE number 4143109
scientific article