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

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.Applied mathematicsStatistics and ProbabilityElectrical Engineering, Mathematics and Computer Scienc