2014/12/29 by Shuang Shen, Shen, Shuang
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Chaos control and synchronization #Complex Systems and Time Series Analysis #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Metric Geometry (math.MG) #Primary 28A80 #Probability (math.PR) #Secondary 28A78
paper · pdf · doi:10.48550/arxiv.1412.8295
openalex publication_date 2014/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a previous work \citeShe we constructed measures on symbolic spaces which satisfy an extended multifractal formalism (in the sense that Olsen's functions b and B differ and that their Legendre transforms have the expected interpretation in terms of dimensions). These measures are composed with a Gray code and projected onto the unit interval so to get doubling measures. Then we were able to show that the projected measure has the same Olsen's functions as the one it comes from and that it also fulfills the extended multifractal formalism. Here we show that the use of a Gray code is not necessary to get these results, although dealing with non doubling measures.