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Session 16. Ergodic Theory and Dynamical Systems
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No semiconjugacy to a map of constant slope |
Michał Misiurewicz, Indiana University-Purdue University Indianapolis, USA
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The talk is based on the joint work with Samuel Roth
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We study countably piecewise continuous, piecewise monotone interval
maps. We establish a necessary and sufficient criterion for the
existence of a nondecreasing semiconjugacy to a map of constant
slope in terms of the existence of an eigenvector of an operator
acting on a space of measures. Then we give sufficient conditions
under which this criterion is not satisfied. Finally, we give
examples of maps not semiconjugate to a map of constant slope via a
nondecreasing map. Our examples are continuous and transitive.
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