| Abstrakt: |
Assume that T n is the full transformation semigroup of X = { 1 , ... , n } and S n ⊂ T n is the symmetric group. For σ ∈ S n and i ∈ X we define f i , σ ∈ T n by f i , σ (i) = σ (i) , and f i , σ (j) = j for j ≠ i. Let S be the subsemigroup of T n generated by idempotents { f 1 , σ , ... , f n , σ } . Let α ∈ S . We study the sequence (card F (α k)) k ∈ N , where F (α k) is the set of fixed points of α k . We will focus on the case σ = (1 2 ... n) . Our motivation comes from a geometric method for detecting chaotic dynamics based on the Ważewski retract principle. [ABSTRACT FROM AUTHOR] |
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