Rigidity of smooth one-sided Bernoulli endomorphisms
نویسندگان
چکیده
A measure-preserving endomorphism is one-sided Bernoulli if it is isomorphic to a noninvertible Bernoulli shift. We show that in piecewise smooth settings this property is very strong and far more subtle than the weak Bernoulli property, by extending of results of W. Parry and P. Walters and proving new results based on continuity of the Radon-Nikodym derivative. In particular, we provide tests which work for noninvariant measures if an invariant measure equivalent to a natural measure exists but its density function is not known. Examples of families of interval maps and complex maps on the Riemann sphere illustrate the results.
منابع مشابه
On the Isomorphism Problem of P-endomorphisms Table of Contents
On the Isomorphism Problem of p-Endomorphisms Peter Jong, Ph.D. Department of Mathematics, University of Toronto, 2003 Let X = (X,B, μ, T ) be a measure-preserving system on a Lebesgue probability space. Given a fixed probability vector p = (p1, . . . , ps), we say that X = (X,B, μ, T ) is a pendomorphism if T is s-to-1 a.e. and the conditional probabilities of the preimages are precisely the c...
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