Dynamical systems can be defined on combinatorial objects; see for example graph dynamical system.
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Fogg, N. Pytheas , Substitutions in dynamics, arithmetics and combinatorics , Lecture Notes in Mathematics, , Berlin: Springer-Verlag, doi : Forman, Robin , "Combinatorial vector fields and dynamical systems", Mathematische Zeitschrift , 4 : —, doi : Kaimanovich, V. Bunch Apr 1 '11 at I found it beautifully written and very accessible. You should find many pointers to the literature in it. Well I'm hoping I gave you enough reading for some time. Sign up or log in Sign up using Google.
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