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We revisit the well-known and much studied Riesz product representation of the Thue-Morse diffraction measure, which is also the maximal spectral measure for the corresponding dynamical spectrum in the complement of the pure point part. The known scaling relations are summarised, and some new findings are explained.
The classic Thue--Morse measure is a paradigmatic example of a purely singular continuous probability measure on the unit interval. Since it has a representation as an infinite Riesz product, many aspects of this measure have been studied in the past
We show that Hamiltonian monodromy of an integrable two degrees of freedom system with a global circle action can be computed by applying Morse theory to the Hamiltonian of the system. Our proof is based on Takenss index theorem, which specifies how
We show that, with the exception of the words $a^2ba^2$ and $b^2ab^2$, all (finite or infinite) binary patterns in the Prouhet-Thue-Morse sequence can actually be found in that sequence as segments (up to exchange of letters in the infinite case). Th
Let $b ge 2$ and $ell ge 1$ be integers. We establish that there is an absolute real number $K$ such that all the partial quotients of the rational number $$ prod_{h = 0}^ell , (1 - b^{-2^h}), $$ of denominator $b^{2^{ell+1} - 1}$, do not exceed $exp(K (log b)^2 sqrt{ell} 2^{ell/2})$.
We propose and analyse a mathematical measure for the amount of squeezing contained in a continuous variable quantum state. We show that the proposed measure operationally quantifies the minimal amount of squeezing needed to prepare a given quantum s