Orbit complexity and data compression

Stefano Galatolo

doi:10.3934/dcds.2001.7.477

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2001, Volume 7, Issue 3: 477-486. Doi: 10.3934/dcds.2001.7.477

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Orbit complexity and data compression

Stefano Galatolo^1,

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

Revised: November 2000

Published: July 2001

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Abstract

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.

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Mathematics Subject Classification: 28D20, 58F13, 68P30.

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