On expanding endomorphisms of the circle. II (Q2716463)

This paper deals with the problem of finding complete measure theoretic invariants for isomorphisms. Note that in his well-known work the first author gave necessary and sufficient conditions for two real analytic Lebesgue measure-preserving expanding endomorphisms of the circle to be isomorphic up to phase factor [Part I, J. Lond. Math. Soc. (2) 41, 272-282 (1990; Zbl 0666.58036) and Ill. J. Math. 44, 516-519 (2000; Zbl 0967.37027)]. Here the authors give sufficient conditions for weak isomorphism of Lebesgue measure-preserving expanding endomorphisms of \(S^1\) giving a partial answer to a question of \textit{M. Shub} and \textit{D. P. Sullivan} [Ergodic Theory Dyn. Syst. 5, 285-289 (1985; Zbl 0583.58022)].