On ergodic theory of A. Schmidt's complex continued fractions over Gaussian field (Q1097305)
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scientific article; zbMATH DE number 4033852
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On ergodic theory of A. Schmidt's complex continued fractions over Gaussian field |
scientific article; zbMATH DE number 4033852 |
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On ergodic theory of A. Schmidt's complex continued fractions over Gaussian field (English)
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1988
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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.
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natural extension transformation
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complex continued fractions
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geodesics
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invariant measure
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