Calculating topological entropy for transient chaos with an application to communicating with chaos

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 57, Issue 6, 1998, Pages 6577-6588

  Jacobs, Joeri ^a   Ott, Edward ^a   Hunt, Brian R ^a  

^a Bldg 142   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000621770     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.57.6577     Document Type: Article

References (22)

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21. See also E. Bollt, Y.-C. Lai, and C. Grebogi, Phys. Rev. Lett. 79, 3787 (1997).
22. This is consistent with J. Vollmer and W. Breymann, Europhys. Lett. 27, 23 (1994). This paper considers the parameter dependence of the entropy of a chaotic attractor. As the parameter increases, more orbits are forbidden, pruned. At the onset of pruning, i.e., the critical parameter beyond which orbits in the chaotic attractor are forbidden, it is shown that the decrease of the topological entropy satisfies a power law behavior. The scaling exponent is shown to be the pointwise dimension of the first pruned orbit. For the one-dimensional map we consider here, pruning starts as soon as the size of the gap is strictly positive. Since the pointwise dimension of any point on the original attractor is one, the scaling exponent should be one as well. This is clearly the case in Eq. (41). EULEEJ