Regularity of Minkowski's question mark measure, its inverse and a class of IFS invariant measures | Zendy

Mantica Giorgio | Zendy; Totik Vilmos | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

Regularity of Minkowski's question mark measure, its inverse and a class of IFS invariant measures

Author(s) -

Mantica Giorgio,

Totik Vilmos

Publication year - 2019

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/jlms.12197

Subject(s) - mathematics , iterated function system , minkowski space , measure (data warehouse) , conjecture , logarithm , invariant (physics) , pure mathematics , iterated function , class (philosophy) , inverse , invariant measure , discrete mathematics , cardinality (data modeling) , combinatorics , mathematical analysis , ergodic theory , attractor , geometry , database , artificial intelligence , computer science , mathematical physics , data mining

We prove the recent conjecture that Minkowski's question mark measure is regular in the sense of logarithmic potential theory. The proof employs: an Iterated Function System composed of Möbius maps, which yields the classical Stern–Brocot sequences, an estimate of the cardinality of large spacings between numbers in these sequences and a criterion due to Stahl and Totik. We also generalize this result to a class of balanced measures of Iterated Function Systems in one dimension.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research