We give a construction of a self-similar tiling of the plane with any prescribed expansion coefficient λ ∈ C (satisfying the necessary algebraic condition of being a complex Perron number). For any integer m > 1 we show that there exists a self-similar tiling with 2π/m-rotational symmetry group and expansion λ if and only if either λ or λe is a complex Perron number for which e is in Q[λ], resp...

We show that the Witt class of a weakly group-theoretical non-degenerate braided fusion category belongs to the subgroup generated by classes of non-degenerate pointed braided fusion categories and Ising braided categories. This applies in particular to solvable nondegenerate braided fusion categories. We also give some sufficient conditions for a braided fusion category to be weakly group-theo...

In this paper we demonstrate the application of the Frobenius-Perron operator to the statistical analysis of chaotic systems. The Frobenius-Perron operator is the main analysis tool whenever statistical properties of the generated and processed signals are of interest. One important eld of application are systems, where information is located in a particular statistic of the chaotic signal. For...

A cycle expansion technique for discrete sums of several PF operators, similar to the one used in the standard classical dynamical zeta-function formalism is constructed. It is shown that the corresponding expansion coefficients show an interesting universal behavior, which illustrates the details of the interference between the particular mappings entering the sum.