An example of a genuinely discontinuous generically chaotic transformation of the interval

doi:https://doi.org/10.4064/ap-63-2-167-172

Open AccessArticle10.4064/ap-63-2-167-172

An example of a genuinely discontinuous generically chaotic transformation of the interval

Józef Piórek-1996-01-01-Annales Polonici Mathematici

TL;DRAbstract

It is proved that a piecewise monotone transformation of the unit interval (with a countable number of pieces) is generically chaotic. The Gauss map arising in connection with the continued fraction expansions of the reals is an example of such a transfor

Chat with Paper

AI Agents for this Paper

It is proved that a piecewise monotone transformation of the unit interval (with a countable number of pieces) is generically chaotic. The Gauss map arising in connection with the continued fraction expansions of the reals is an example of such a transfor

Keywords

MathematicsCountable setUnit intervalInterval (graph theory)ChaoticTransformation (genetics)PiecewisePure mathematics

Chat

Click to start Chat