The duration of transients

Pelikan, S.

doi:10.1090/S0002-9947-1985-0766215-4

The duration of transients
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by S. Pelikan

Trans. Amer. Math. Soc. 287 (1985), 215-221

DOI: https://doi.org/10.1090/S0002-9947-1985-0766215-4

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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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