On the modulus of continuity for spectral measures in substitution dynamics. (English) Zbl 1339.37004

Bufetov, Alexander I.; Solomyak, Boris

Adv. Math. 260, 84-129 (2014).

In the paper under review some properties (like modulus of continuity and dimension-like) of spectral measure of suspension flows over substitution dynamical systems are investigated. One of the main results gives a Hölder property of spectral measures of self-similar suspension flows at zero with explicitly computed Hölder exponent.

Reviewer: Ivan Podvigin (Novosibirsk)

MSC:

37A30	Ergodic theorems, spectral theory, Markov operators
37B10	Symbolic dynamics
37E35	Flows on surfaces
28A78	Hausdorff and packing measures

Keywords:

substitution dynamical system; spectral measure; Hölder continuity; Diophantine approximation; Bernoulli convolution

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