[La fonction de complexité comme invariant topologique des espaces de pavages]
Il est prouvé dans cet article que deux pavages apériodiques et répétitifs dont les espaces de pavages sont homéomorphes ont des fonctions de complexité asymptotiquement équivalentes en un certain sens. Cela implique que lorsque les fonctions de complexité croissent polynomialement, l’exposant du terme dominant est préservé par homéomorphisme. Ce théorème peut s’énoncer en termes de mots infinis
It is proved that whenever two aperiodic repetitive tilings with finite local complexity have homeomorphic tiling spaces, their associated complexity functions are asymptotically equivalent in a certain sense (which implies, if the complexity is polynomial, that the exponent of the leading term is preserved by homeomorphism). This theorem can be reworded in terms of
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Keywords: aperiodic tilings, complexity, repetitivity, flow-equivalence, orbit-equivalence
Mots-clés : pavages apériodiques, complexité, répétitivité, équivalence de flot, équivalence d’orbite
Julien, Antoine 1

@article{AIF_2017__67_2_539_0, author = {Julien, Antoine}, title = {Complexity as a homeomorphism invariant for tiling spaces}, journal = {Annales de l'Institut Fourier}, pages = {539--577}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {67}, number = {2}, year = {2017}, doi = {10.5802/aif.3091}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3091/} }
TY - JOUR AU - Julien, Antoine TI - Complexity as a homeomorphism invariant for tiling spaces JO - Annales de l'Institut Fourier PY - 2017 SP - 539 EP - 577 VL - 67 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3091/ DO - 10.5802/aif.3091 LA - en ID - AIF_2017__67_2_539_0 ER -
%0 Journal Article %A Julien, Antoine %T Complexity as a homeomorphism invariant for tiling spaces %J Annales de l'Institut Fourier %D 2017 %P 539-577 %V 67 %N 2 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3091/ %R 10.5802/aif.3091 %G en %F AIF_2017__67_2_539_0
Julien, Antoine. Complexity as a homeomorphism invariant for tiling spaces. Annales de l'Institut Fourier, Tome 67 (2017) no. 2, pp. 539-577. doi : 10.5802/aif.3091. https://aif.centre-mersenne.org/articles/10.5802/aif.3091/
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