Number of Forts in Iterated Logistic Mapping

Abstract EN

Using the theory of complete discrimination system and the computer algebra system MAPLE V.17, we compute the number of forts for the logistic mapping f λ ( x ) = λ x ( 1 - x ) on [ 0,1 ] parameterized by λ ∈ ( 0,4 ] .

We prove that if 0 < λ ≤ 2 then the number of forts does not increase under iteration and that if λ > 2 then the number of forts is not bounded under iteration.

Furthermore, we focus on the case of λ > 2 and give for each k = 1 , … , 7 some critical values of λ for the change of numbers of forts.