Finding infinitely many even or odd continued fractions by introducing a new family of maps

Master thesis (2015)

Contributors

C. Kraaikamp (mentor)
Programme
Applied mathematics (EEMCS) (TU Delft)
Copyright: © 2015 Langeveld, N.D.S.
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Published Date

22-05-2015

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Programme

Applied mathematics

Abstract

A new family of continued fractions expansions is introduced by combining two existing family's (2-expansions and flipped expansions). This new family has infinitely many mappings with the property that for every x the digits are only even or only odd. Apart from a whole range of examples, convergence is proved and ergodicity is studied. By building the natural extension the invariant measure of a lot of examples have been obtained. In the last Chapter a new way of approximating the density is introduced by using the Gauss Kuzmin theorem. This method is applied to continued fraction expansions where the corresponding map has a fininte number of branches.