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Entropy 2012, 14(4), 742-768; doi:10.3390/e14040742
Article

Computing the Topological Entropy of Multimodal Maps via Min-Max Sequences

1,* , 2
 and 1
1 Centro de Investigación Operativa, Universidad Miguel Hernández, Avda. de la Universidad s/n, 03202 Elche, Spain 2 NonLinear Dynamics Group, IST, Department of Physics, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
* Author to whom correspondence should be addressed.
Received: 9 February 2012 / Revised: 30 March 2012 / Accepted: 2 April 2012 / Published: 18 April 2012
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Abstract

We derive an algorithm to recursively determine the lap number (minimal number of monotonicity segments) of the iterates of twice differentiable l-modal map, enabling to numerically calculate the topological entropy of these maps. The algorithm is obtained by the min-max sequences—symbolic sequences that encode qualitative information about all the local extrema of iterated maps.
Keywords: topological entropy; interval maps; multimodal maps topological entropy; interval maps; multimodal maps
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.

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MDPI and ACS Style

Amigó, J.M.; Dilão, R.; Giménez, Á. Computing the Topological Entropy of Multimodal Maps via Min-Max Sequences. Entropy 2012, 14, 742-768.

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