Orbit complexity and data compression

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July 2001, 7(3): 477-486. doi: 10.3934/dcds.2001.7.477

Orbit complexity and data compression

1.	Dipartimento di Matematica Applicata, Università di Pisa, Via Bonanno Pisano

Revised November 2000 Published April 2001

Abstract
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We consider data compression algorithms as a tool to get an approximate measure for the quantity of information contained in a string. By this it is possible to give a notion of orbit complexity for topological dynamical systems. In compact ergodic dynamical systems, entropy is almost everywhere equal to orbit complexity. The use of compression algorithms allows a direct estimation of the information content of the orbits.

Keywords: entropy, Topological dynamical systems, information, orbit complexity., coding.

Mathematics Subject Classification: 28D20, 58F13, 68P3.

Citation: Stefano Galatolo. Orbit complexity and data compression. Discrete & Continuous Dynamical Systems - A, 2001, 7 (3) : 477-486. doi: 10.3934/dcds.2001.7.477

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