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

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

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 𝑇𝜙∶=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 occurrenc...

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Main Authors: Maria F. Correia, Carlos C. Ramos, Sandra Vinagre
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2012/796180
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spelling doaj-c48802d9b3594ea79bdf6c57b4096d502020-11-24T23:18:58ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/796180796180Iteration of Differentiable Functions under m-Modal Maps with Aperiodic Kneading SequencesMaria F. Correia0Carlos C. Ramos1Sandra Vinagre2CIMA-UE and Department of Mathematics, University of Évora, Rua Romão Ramalho 59, 7000-671 Évora, PortugalCIMA-UE and Department of Mathematics, University of Évora, Rua Romão Ramalho 59, 7000-671 Évora, PortugalCIMA-UE and Department of Mathematics, University of Évora, Rua Romão Ramalho 59, 7000-671 Évora, PortugalWe 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 𝑇𝜙∶=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.http://dx.doi.org/10.1155/2012/796180
collection DOAJ
language English
format Article
sources DOAJ
author Maria F. Correia
Carlos C. Ramos
Sandra Vinagre
spellingShingle Maria F. Correia
Carlos C. Ramos
Sandra Vinagre
Iteration of Differentiable Functions under m-Modal Maps with Aperiodic Kneading Sequences
International Journal of Mathematics and Mathematical Sciences
author_facet Maria F. Correia
Carlos C. Ramos
Sandra Vinagre
author_sort Maria F. Correia
title Iteration of Differentiable Functions under m-Modal Maps with Aperiodic Kneading Sequences
title_short Iteration of Differentiable Functions under m-Modal Maps with Aperiodic Kneading Sequences
title_full Iteration of Differentiable Functions under m-Modal Maps with Aperiodic Kneading Sequences
title_fullStr Iteration of Differentiable Functions under m-Modal Maps with Aperiodic Kneading Sequences
title_full_unstemmed Iteration of Differentiable Functions under m-Modal Maps with Aperiodic Kneading Sequences
title_sort iteration of differentiable functions under m-modal maps with aperiodic kneading sequences
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2012-01-01
description 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 𝑇𝜙∶=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.
url http://dx.doi.org/10.1155/2012/796180
work_keys_str_mv AT mariafcorreia iterationofdifferentiablefunctionsundermmodalmapswithaperiodickneadingsequences
AT carloscramos iterationofdifferentiablefunctionsundermmodalmapswithaperiodickneadingsequences
AT sandravinagre iterationofdifferentiablefunctionsundermmodalmapswithaperiodickneadingsequences
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