computing the topological entropy of multimodal maps via min-max sequences计算多通道通过min-max序列映射的拓扑熵.pdfVIP

Entropy 2012, 14, 742-768; doi:10.3390/ OPEN ACCESS entropy ISSN 1099-4300 /journal/entropy Article Computing the Topological Entropy of Multimodal Maps via Min-Max Sequences 1, 2 1 ´ ´ ´ ´ ˜ ´ Jose Marıa Amigo *, Rui Dilao and Angel Gimenez 1 ´ ´ Centro de Investigacion Operativa, Universidad Miguel Hernandez, Avda. de la Universidad s/n, 03202 Elche, Spain; E-Mail: a.gimenez@umh.es 2 NonLinear Dynamics Group, IST, Department of Physics, Av. Rovisco Pais, 1049-001 Lisbon, Portugal; E-Mail: rui@sd.ist.utl.pt * Author to whom correspondence should be addressed; E-Mail: jm.amigo@umh.es; Tel.: +34-96-665-8911; Fax: +34-96-665-8715. Received: 9 February 2012; in revised form: 30 March 2012 / Accepted: 2 April 2012 / Published: 18 April 2012 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 1. Introduction Entropy is a ubiquitous tool in physics and mathematics. It measures