A simplified algorithm for the topological entropy of multimodal maps

TL;DR

This paper introduces a simplified numerical algorithm for computing the topological entropy of multimodal maps, improving upon previous methods by utilizing a closed formula with min-max symbols, and demonstrates its effectiveness through benchmarking.

Contribution

The paper presents a new, simplified algorithm for calculating topological entropy of multimodal maps, extending previous methods and benchmarking its performance.

Findings

The new algorithm is more efficient than the previous one for multimodal maps.

Benchmark results show the new algorithm outperforms the old one in most cases.

The algorithm is less effective in the unimodal case.

Abstract

A numerical algorithm to compute the topological entropy of multimodal maps is proposed. This algorithm results from a closed formula containing the so-called min-max symbols, which are closely related to the kneading symbols. Furthermore, it simplifies a previous algorithm, also based on min-max symbols, which was originally proposed for twice differentiable multimodal maps. The new algorithm has been benchmarked against the old one with a number of multimodal maps, the results being reported in the paper. In particular, the comparison is favorable to the new algorithm, except in the unimodal case.