Abstract
The standard encoding procedure to describe the chaotic orbits of unimodal maps is accurately investigated. We show that the grammatical rules of the underlying language can be easily classified in a compact form by means of a universal parameter τ. Two procedures to construct finite graphs which approximate non-Markovian cases are discussed, showing also the intimate relation with the corresponding construction of approximate Markov partitions. The convergence of the partial estimates of the topological entropy is discussed, proving that the error decreases exponentially with the length of the sequences considered. The rate is shown to coincide with the topological entropyh itself. Finally, a superconvergent method to estimateh is introduced.
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Isola, S., Politi, A. Universal encoding for unimodal maps. J Stat Phys 61, 263–291 (1990). https://doi.org/10.1007/BF01013965
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DOI: https://doi.org/10.1007/BF01013965