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Topological and combinatorial properties of finite rank minimal subshifts

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Topological and combinatorial properties of finite rank minimal subshifts
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15
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You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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This talk is about topological and combinatorial properties of finite rank minimal systems. We establish a clear connection with the S -adic subshifts and provide necessary and sufficient conditions for a subshift to be of finite rank. Using these conditions we study the number of asympototic components of a finite rank subshift and show that there is a rank two subshift with non superlinear complexity. I will also mention results concerning the automorphism group of a finite rank subshift. This is work in progress with Fabien Durand, Alejandro Maass and Samuel Petite.