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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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/796180 |
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| author | Maria F. Correia Carlos C. Ramos Sandra Vinagre |
| author_facet | Maria F. Correia Carlos C. Ramos Sandra Vinagre |
| author_sort | Maria F. Correia |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-c48802d9b3594ea79bdf6c57b4096d50 |
| institution | DOAJ |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-c48802d9b3594ea79bdf6c57b4096d502025-08-20T03:23:06ZengWileyInternational 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2012/796180 |
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