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On Expanding Endomorphisms of the Circle
Author(s) -
Cowen Robert
Publication year - 1990
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/s2-41.2.272
Subject(s) - endomorphism , measure (data warehouse) , lebesgue measure , jacobian matrix and determinant , mathematics , isomorphism (crystallography) , pure mathematics , invariant (physics) , character (mathematics) , lebesgue integration , topology (electrical circuits) , algebra over a field , discrete mathematics , computer science , combinatorics , data mining , geometry , mathematical physics , crystal structure , chemistry , crystallography
In this paper we investigate a problem posed by M. Shub and D. Sullivan on the classification of real analytic Lebesgue measure‐preserving endomorphisms of the circle. We introduce a new Jacobian invariant that enables us to study the phase factor. Finally, we introduce complete measure‐theoretic isomorphism invariants which turn out to be simultaneously measure‐theoretic and topological in character.