Conductance and Noncommutative Dynamical Systems |
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Authors: | C Correia Ramos Nuno Martins J Sousa Ramos |
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Institution: | 1. Departamento de Matemática, Universidade de évora, Rua Rom?o Ramalho 59, 7000-671, évora, Portugal 2. Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1, 1049-001, Lisboa, Portugal
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Abstract: | In this work, we introduce the notion of conductance in the context of Cuntz–Krieger C∗-algebras. These algebras can be seen as a noncommutative version of topological Markov chains. Conductance is a useful notion
in the theory of Markov chains to study the approach of a system to the equilibrium state. Our goal is twofold. On one hand,
conductance can be used to measure the complexity of dynamical systems, complementing topological entropy. On the other hand,
using C∗-algebras, we can give a natural framework to analyze the path space of a finite graph associated to a Markov shift. |
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Keywords: | conductance in C*-algebras Cuntz– Krieger C*-algebras Markov shift noncommutative dynamical systems topological entropy |
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