Symbolic Dynamics and Sarkovskii’s Theorem

    Abstract

    All spaces are metric spaces. A dynamical system is a pair (X, f) consisting of a space X and a continuous map f : X → X . For x ∈ X define the orbit of x as O (x) = { f(x) : n ∈ N } . We say x ∈ X is periodic with period n > 0 iff f(x) = x . Such n is called a period of x , and the least period is sometimes called the prime period (although it need not be… (More)

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