Proposition 1.1. If Xo has minimal period q then the orbit of Xo consists of q...

  

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Proposition 1.1. If Xo has minimal period q then the orbit of Xo consists of q distinct points Xo, X₁, Xq-1 repeated periodically and each of the points Xi is also periodic of minimal period q. ..... If Xo has period q then it also has period p = 2q, 3q,..., kq,..., that is, it also returns to its initial state after times which are multiples of q. Similarly, having found some period p, the minimal period must be a divisor of p. For example, a point with F¹2(X) = Xo could have minimal period q = 1, 2, 3, 4, 6 or 12. Proposition 1.1. If Xo has minimal period q then the orbit of Xo consists of q distinct points Xo, X₁, Xq-1 repeated periodically and each of the points Xi is also periodic of minimal period q. ..... If Xo has period q then it also has period p = 2q, 3q,..., kq,..., that is, it also returns to its initial state after times which are multiples of q. Similarly, having found some period p, the minimal period must be a divisor of p. For example, a point with F¹2(X) = Xo could have minimal period q = 1, 2, 3, 4, 6 or 12.

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Solution If Xo has minimal peri... View the full answer