On ergodic theory of A. Schmidt's complex continued fractions over Gaussian field
We consider a transformation associated with \textit{A. L. Schmidt}'s complex continued fractions [ibid. 93, 39--62 (1982; Zbl 0467.10038)]. We discuss a relation between complex continued fractions and geodesics over a three dimensional hyperbolic space and give an absolutely continuous ergodic invariant measure for the transformation. As an application, we show some properties of complex continued fractions.
scientific article; zbMATH DE number 4033852