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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The duration of transients


Author: S. Pelikan
Journal: Trans. Amer. Math. Soc. 287 (1985), 215-221
MSC: Primary 58F11
DOI: https://doi.org/10.1090/S0002-9947-1985-0766215-4
MathSciNet review: 766215
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Abstract: A transformation $ T$ defined on $ X \subset {{\mathbf{R}}^n}$ for which $ T(X) \supset X$ is considered. A transient in $ X$ is a trajectory $ x,Tx, \ldots ,{T^m}x \subset X$ so that $ {T^{m + 1}}x \notin X$. In this case, $ m$ is the duration of the transient. A method for estimating the average duration of transients is given, and an example of a transformation with exceedingly long transients is described.


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DOI: https://doi.org/10.1090/S0002-9947-1985-0766215-4
Article copyright: © Copyright 1985 American Mathematical Society