Estimating topological entropy from individual orbits

Abstract

The relationship between the topological entropy of a continuous piecewise monotone interval map and the permutation entropy of its orbits is given. We use this relationship to estimate the topological entropy of the map.

Keywords:

• topological entropy
• permutations
• interval maps
• numerical chaos
• entropy estimation

2000 AMS Subject Classifications :

• 37E05
• 37B40
• 26A18
• 65P20

Acknowledgements

This paper has been partially supported by the grants MTM2008-03679/MTM [MCI (Ministerio de Ciencia e Innovación) and FEDER (Fondo Europeo de Desarrollo Regional)] and 08667/PI/08 [Fundación Séneca, CARM].