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math.DS2018
Combinatorial Proof of Kakutani's Fixed Point Theorem
Yitzchak Shmalo
Kakutani's fixed point theorem is a generalization of Brouwer's fixed point theorem to upper semicontinuous multivalued maps and is used extensively in game theory and other areas…
math.DS2017
Combinatorial approach to detection of fixed points, periodic orbits, and symbolic dynamics
Marian Gidea, Yitzchak Shmalo
We present a combinatorial approach to rigorously show the existence of fixed points, periodic orbits, and symbolic dynamics in discrete-time dynamical systems, as well as to find…