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Observing expansive maps
Author(s) -
Achigar Mauricio,
Artigue Alfonso,
Monteverde Ignacio
Publication year - 2018
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms.12134
Subject(s) - injective function , expansive , observability , mathematics , dimension (graph theory) , pure mathematics , metric space , uniqueness , space (punctuation) , metric (unit) , discrete mathematics , topology (electrical circuits) , computer science , combinatorics , mathematical analysis , compressive strength , operations management , materials science , economics , composite material , operating system
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. 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.