Iteration of Differentiable Functions under m -Modal Maps with Aperiodic Kneading Sequences

Maria F. Correia, Carlos C. Ramos and Sandra Vinagre

International Journal of Mathematics and Mathematical Sciences, 2012, vol. 2012, 1-17

Abstract:

We consider the dynamical system ( ð ’œ , 𠑇 ), where ð ’œ is a class of differentiable functions defined on some interval and 𠑇 : ð ’œ → ð ’œ is the operator 𠑇 𠜙 ∶ = ð ‘“ ∘ 𠜙 , where ð ‘“ is a differentiable m -modal map. Using an algorithm, we obtained some numerical and symbolic results related to the frequencies of occurrence of critical values of the iterated functions when the kneading sequences of ð ‘“ are aperiodic. Moreover, we analyze the evolution as well as the distribution of the aperiodic critical values of the iterated functions.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:796180

DOI: 10.1155/2012/796180

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