Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Orbit complexity and data compression

Pages: 477 - 486, Volume 7, Issue 3, July 2001      doi:10.3934/dcds.2001.7.477

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Stefano Galatolo - Dipartimento di Matematica Applicata, Università di Pisa, Via Bonanno Pisano, Italy (email)

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.

Keywords:  Topological dynamical systems, information, coding, entropy, orbit complexity.
Mathematics Subject Classification:  28D20, 58F13, 68P30.

Revised: November 2000;      Available Online: April 2001.