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International Journal of Mathematics and Mathematical Sciences
Volume 2012, Article ID 796180, 17 pages
Research Article

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

CIMA-UE and Department of Mathematics, University of Évora, Rua Romão Ramalho 59, 7000-671 Évora, Portugal

Received 30 March 2012; Accepted 21 May 2012

Academic Editor: Hans Engler

Copyright © 2012 Maria F. Correia et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider the dynamical system ( 𝒜 , 𝑇 ), where 𝒜 is a class of differentiable functions defined on some interval and 𝑇 : 𝒜 𝒜 is the operator 𝑇 𝜙 = 𝑓 𝜙 , where 𝑓 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 𝑓 are aperiodic. Moreover, we analyze the evolution as well as the distribution of the aperiodic critical values of the iterated functions.