20 citations · 48 across the 17 of their papers we have counts for
20 papers
Renormalisation techniques for inflation systems and some of their applications
Michael Baake, Franz Gähler, Anna Klick +2
Exact renormalisation techniques are important and powerful, particularly for inflation-generated systems. We review recent results in this direction. We recall the necessary notio…
Radius-zero Extended Symmetries and Irregular Fibres of -Substitution Subshifts
Álvaro Bustos-Gajardo, Daniel Luz, Neil Mañibo
In this work, we consider -shifts generated by digit substitutions. For such a shift , we study the elements of the normaliser of in the gr…
On the full centraliser of Erdős $\cB$-free shifts
Michael Baake, Neil Mañibo
The sets of $\cB$-free integers are considered with respect to (reversing) symmetries. It is well known that, for a large class of them, the centraliser of the associated $\cB$-fre…
Substitutions and their generalisations
Neil Mañibo
Tilings and point sets arising from substitutions are classical mathematical models of quasicrystals. Their hierarchical structure allows one to obtain concrete answers regarding s…
Spectral theory of regular sequences: parametrisation and spectral characterisation
Michael Coons, James Evans, Philipp Gohlke +1
We extend the existence of ghost measures beyond nonnegative primitive regular sequences to a large class of nonnegative real-valued regular sequences. In the general case, where t…
Monochromatic arithmetic progressions in automatic sequences with group structure
Ibai Aedo, Uwe Grimm, Neil Mañibo +2
We determine asymptotic growth rates for lengths of monochromatic arithmetic progressions in certain automatic sequences. In particular, we look at (one-sided) fixed points of aper…
Catalan numbers as discrepancies for a family of substitutions on infinite alphabets
Dirk Frettlöh, Alexey Garber, Neil Mañibo
In this work, we consider a class of substitutions on infinite alphabets and show that they exhibit a growth behaviour which is impossible for substitutions on finite alphabets. Wh…
Torsion-free -adic shifts and their spectrum
Álvaro Bustos-Gajardo, Neil Mañibo, Reem Yassawi
In this work we study -adic shifts generated by sequences of morphisms that are constant-length. We call a sequence of constant-length morphisms torsion-free if any prime diviso…
Substitution tilings with transcendental inflation factor
Dirk Frettlöh, Alexey Garber, Neil Mañibo
For any , we construct a substitution on an infinite alphabet which gives rise to a substitution tiling with inflation factor . In particular, we obtain the first class of…
Substitutions on compact alphabets
Neil Mañibo, Dan Rust, James J. Walton
We develop a systematic approach to continuous substitutions on compact Hausdorff alphabets. Focussing on implications of irreducibility and primitivity, we highlight important fea…
Spectral theory of spin substitutions
Natalie Priebe Frank, Neil Mañibo
We introduce qubit substitutions in , which have non-rectangular domains based on an endomorphism of and a set of coset representativ…
Ghost distributions of regular sequences are affine transformations of self-affine sets
Michael Coons, James Evans, Zachary Groth +1
Ghost measures of regular sequences---the unbounded analogue of automatic sequences---are generalisations of standard fractal mass distributions. They were introduced to determine…
Spectral properties of substitutions on compact alphabets
Neil Mañibo, Dan Rust, James J. Walton
We consider substitutions on compact alphabets and provide sufficient conditions for the diffraction to be pure point, absolutely continuous and singular continuous. This allows on…
Mixing properties and entropy bounds of a family of Pisot random substitutions
Giovanni B. Escolano, Neil Mañibo, Eden Delight Miro
We consider a two-parameter family of random substitutions and show certain combinatorial and topological properties they satisfy. We establish that they admit recognisable words a…
Admissible reversing and extended symmetries for bijective substitutions
Álvaro Bustos, Daniel Luz, Neil Mañibo
In this paper, we deal with reversing and extended symmetries of shifts generated by bijective substitutions. We provide equivalent conditions for a permutation on the alphabet to…
Zeckendorf representations and mixing properties of sequences
Neil Manibo, Eden Miro, Dan Rust +1
We use generalised Zeckendorf representations of natural numbers to investigate mixing properties of symbolic dynamical systems. The systems we consider consist of bi-infinite sequ…
Renormalisation of pair correlation measures for primitive inflation rules and absence of absolutely continuous diffraction
Michael Baake, Franz Gaehler, Neil Manibo
The pair correlations of primitive inflation rules are analysed via their exact renormalisation relations. We introduce the inflation displacement algebra that is generated by the…
Binary constant-length substitutions and Mahler measures of Borwein polynomials
Michael Baake, Michael Coons, Neil Manibo
We show that the Mahler measure of every Borwein polynomial -- a polynomial with coefficients in having non-zero constant term -- can be expressed as a maximal Lyapu…
Spectral analysis of a family of binary inflation rules
Michael Baake, Uwe Grimm, Neil Manibo
The family of primitive binary substitutions defined by with is investigated. The spectral type of the corresponding diffraction measur…
Lyapunov exponents for binary substitutions of constant length
Neil Mañibo
A method of confirming the absence of absolutely continuous diffraction via the positivity of Lyapunov exponents derived from the corresponding Fourier matrices is presented, which…