We investigate combinatorial properties of aperiodic simple Toeplitz subshifts, as well as spectral properties of Jacobi operators defined by them. the underlying action of the corresponding Delone dynamical system is free. In this case, the Delone sets in question are in fact strongly aperiodic, i.e. Our construction applies in particular to all two-step nilpotent Lie groups defined over $\mathbb Q$ such as the Heisenberg group. Building on our previous work, we establish unique ergodicity of the corresponding Delone dynamical systems. These are the first examples of weakly aperiodic linearly repetitive Delone sets in non-abelian Lie groups. We show, by explicit construction, that every RAHOGRASP admits a lattice with a primitive symbolic substitution system and hence contains a weakly aperiodic linearly repetitive Delone set. In this article, we consider a large class of non-abelian nilpotent Lie groups with dilation structures, which we refer to as rationally homogeneous Lie groups with rational spectrum (RAHOGRASPs). Strict validation is up to you.Symbolic substitution systems are an important source of aperiodic Delone sets in abelian locally compact groups. La Métrique de Hausdorff ( TIPE sup 1995-96).Théorème de Sharkovsky ( TIPE spé 1996-97).Homéomorphismes du tore : nombre de rotation ( TIPE spé 1997-98).Classification non-linéaire des espaces de Banach ( mémoire de licence 1998-99).Six facettes de la sphère d'homologie de Poincaré ( mémoire de maîtrise 1999-2000).Aspects quantitatifs du théorème de récurrence de Poincaré ( mémoire de DEA 2000-2001).
#Finite minimal subshift software#
Spreading huge free software without internet connection via self-replicating USB keys ( ExtremeCom 2013).A Universal Oracle for Signal Machines, ( note présented at CiE 2017, Lecture Notes in Computer Science, 10307 (2017), 315-326).Symmetric Determinantal Representations in Characteristic 2 with Bruno Grenet and Stéphan Thomassé ( Linear Alg.Asymptotics for connected graphs and irreducible tournaments with Khaydar Nurligareev ( note présented at Eurocomb 2021, Extended Abstracts EuroComb 2021.From the complexity of infinite permutations to the profile of bichains with Maurice Pouzet ( proceedings of Rogics'08).Minimizing submodular functions with Stéphan Thomassé ( mini-survey for the JCALM 2007).Freeman Digitization and Tangent Word Based Estimators ( note présented at DGCI 2014, Lecture Notes in Computer Science, 8668 (2014), 176-189).Persistent patterns in integer discrete circles with André Hoarau ( note presented at DGCI 2013, Lecture Notes in Computer Science, 7749 (2013), 35-46).The complexity of tangent words ( note presented at WORDS 2011, Electronic Proceedings of Theoretical Computer Science, 63 (2011), 152-157).Another definition for digital tangents ( note presented at DGCI 2011, Lecture Notes in Computer Science, 6607 (2011), 95-103).Rigo (Eds), Encyclopedia of Mathematics and its Applications 135, Cambridge University Press (2010)). Infinite words with uniform frequencies, and invariant measures with Sébastien Ferenczi ( preliminary version of Chapter 7 of the book Combinatorics, Automata and Number Theory, V.Topological Martin's Delirium ( draft answering a question of Martin Lustig).Quasiperiodic infinite words : multi-scale case and dynamical properties with Solomon Marcus ( preprint).Estimating the number of ergodic measures of a minimal subshift knowing the geometry of its Rauzy graphs ( preprint).Everything is illuminated with Samuel Lelièvre et Barak Weiss ( Geometry & Topology, No.Finite blocking property on translation surfaces ( summary of the first 4 papers toward open questions, Oberwolfach Report, No.
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