Symbolic dynamics and rotation numbers

Peter Veerman

Physica A: Statistical Mechanics and its Applications, 1986, vol. 134, issue 3, 543-576

Abstract: In the space of binary sequences, minimal sets, that is: sets invariant under the shift operation, that have no invariant proper subsets, are investigated. In applications, such as a piecewise linear circle map and the Smale horseshoe in a mapping of the annulus, each of these sets is invariant under the mapping. These sets can be assigned a unique rotation number equal to the average of the number of ones in the sequences.

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:134:y:1986:i:3:p:543-576

DOI: 10.1016/0378-4371(86)90015-4

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