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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 (CC BY 3.0).
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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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