A Gauss measure on the set of interval exchange transformations | Zendy

William A. Veech | Zendy

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A 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

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.

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