A BESICOVITCH-MORSE FUNCTION PRESERVING THE LEBESGUE MEASURE

Jozef Bobok (1) , Serge Troubetzkoy (2)

1 KM FSv CVUT
2 I2M - Institut de Mathématiques de Marseille

We continue the investigation of which non-dierentiable maps can occur in the framework of ergodic theory started in [2]. We construct a Besicovitch-Morse function map which preserves the Lebesgue measure. We also show that the set of Besicovitch functions is of rst category in the set of continuous functions which preserve the Lebesgue measure.

Domaines: Systèmes dynamiques [math.DS]

Jozef Bobok, Serge Troubetzkoy. A BESICOVITCH-MORSE FUNCTION PRESERVING THE LEBESGUE MEASURE. 2019. ⟨hal-02162052⟩