Dynamics and Analysis Seminar: Generalized betatransformations and the entropy of unimodal maps
Dynamics and Analysis Seminar
Speaker: Dan Thompson (Ohio State)
Title: Generalized betatransformations and the entropy of unimodal maps
Abstract: Generalized betatransformations are the class of piecewise continuous interval maps given by taking the betatransformation x↦ beta x (mod1), where beta > 1, and replacing some of the branches with branches of constant negative slope. We would like to describe the set of beta for which these maps can admit a Markov partition. We know that beta (which is the exponential of the entropy of the map) must be an algebraic number. Our main result is that the Galois conjugates of such beta have modulus less than 2, and the modulus is bounded away from 2 apart from the exceptional case of conjugates lying on the real line. This extends an analysis of Solomyak for the case of betatransformations, who obtained a sharp bound of the golden mean in that setting.
4:30 PM  6:30 PM EST
 Venue
 Exley Science Center Tower ESC 638
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 Venue Address
 45 Wyllys Avenue, Middletown, CT United States