Measures of maximal entropy for suspension flows over the full shift

  • Tamara KucherenkoEmail author
  • Daniel J. Thompson


We consider suspension flows with continuous roof function over the full shift \(\Sigma \) on a finite alphabet. For any positive entropy subshift of finite type \(Y \subset \Sigma \), we explicitly construct a roof function such that the measure(s) of maximal entropy for the suspension flow over \(\Sigma \) are exactly the lifts of the measure(s) of maximal entropy for Y. In the case when Y is transitive, this gives a unique measure of maximal entropy for the flow which is not fully supported. If Y has more than one transitive component, all with the same entropy, this gives explicit examples of suspension flows over the full shift with multiple measures of maximal entropy. This contrasts with the case of a Hölder continuous roof function where it is well known the measure of maximal entropy is unique and fully supported.

Mathematics Subject Classification

37D35 37B10 37A35 



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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsThe City College of New YorkNew YorkUSA
  2. 2.Department of MathematicsOhio State UniversityColumbusUSA

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