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arXiv · 1611.08488

Observing expansive maps

Mauricio Achigar·Alfonso Artigue·Ignacio Monteverde
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Abstract

We consider the problem of the observability of positively expansive maps by the time series associated to continuous real functions. For this purpose we prove a general result on the generic observability of a locally injective map of a compact metric space of finite topological dimension, extending earlier work by Gutman [6]. We apply this result to partially solve the problem of finding the minimal number of functions needed to observe a positively expansive map. We prove that two functions are necessary and sufficient for positively expansive maps on tori.

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Mauricio Achigar, Alfonso Artigue, Ignacio Monteverde. 2016-11-25. Observing expansive maps. https://arxiv.org/abs/1611.08488

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