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

Orbit complexity and data compression

Stefano Galatolo 1,

1. 

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

Revised  November 2000 Published  April 2001

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