Open AccessA Gauss measure on the set of interval exchange transformations
Author(s) -
William A. Veech
Publication year - 1981
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.78.2.696
Subject(s) - ergodic theory , gauss , measure (data warehouse) , interval (graph theory) , mathematics , invariant measure , invariant (physics) , ergodicity , class (philosophy) , transformation (genetics) , pure mathematics , combinatorics , computer science , statistics , physics , artificial intelligence , chemistry , biochemistry , quantum mechanics , database , mathematical physics , gene
An interval exchange transformation is a piece-wise order-preserving isometry of a finite interval. In previous works the author has reduced certain questions about interval exchange transformations to questions about the ergodic behavior of a related class of transformations, with domain the body of all interval exchange transformations. The latter questions can be answered with the aid of Gauss measures for the related transformations; by Gauss measure is understood a conservative, ergodic invariant measure whose density is a rational function. The present note describes the construction of such Gauss measures.