Information and dynamical systems: a concrete measurement on sporadic dynamics |
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| Institution: | 1. Dipartimento di Matematica, Università di Pisa, Via Buonarroti 2/a, 56127 Pisa, Italy;2. Dipartimento di Matematica Applicata, Università di Pisa, Via Bonanno Pisano 25/b, 56126 Pisa, Italy;3. Centro Interdisciplinare per lo Studio dei Sistemi Complessi (CISSC), Università di Pisa, Via Bonanno Pisano 25/b, 56126 Pisa, Italy;1. Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya, 464-8602, Japan;2. Keio Institute of Pure and Applied Sciences (KiPAS), Department of Mathematics, Keio University, Yokohama, 223-8522, Japan;1. Institute of Geosciences and Earth Resources (IGG) – National Research Council (CNR), Via Valperga Caluso 35, 10125 Turin, Italy;2. Institute of Geosciences and Earth Resources (IGG) – National Research Council (CNR), Via Giuseppe Moruzzi 1, 56124 Pisa, Italy |
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| Abstract: | We present a method for the study of dynamical systems based on the notion of quantity of information. Measuring the quantity of information of a string by using data compression algorithms, it is possible to give a notion of orbit complexity of dynamical systems. In compact ergodic dynamical systems, entropy is almost everywhere equal to orbit complexity. We have introduced a new compression algorithm called CASToRe which allows a direct estimation of the information content of the orbits in the 0-entropy case. The method is applied to a sporadic dynamical system (Manneville map). |
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