A Besicovitch-Morse function preserving the Lebesgue measure

2019/06/24 by Jozef Bobok, Bobok, Jozef, Serge Troubetzkoy +1
Mathematics · Economics, Econometrics and Finance · #Mathematical Dynamics and Fractals #Advanced Topology and Set Theory #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1906.09804

Abstract

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.

Related

• A theorem of Besicovitch and a generalization of the Birkhoff Ergodic Theorem
• Besicovitch-Morse type covering lemmas in metric spaces
• Doubly invariant subspaces of the Besicovitch space
• "Barcodes" for continuous maps and a brief introduction to Alternative Morse Theory
• Measure Preserving Diffeomorphisms of the Torus are Unclassifiable