Observing expansive maps

Autor:	Mauricio Achigar, Alfonso Artigue, Ignacio Monteverde
Rok vydání:	2018
Předmět:	Discrete mathematics Pure mathematics Series (mathematics) General Mathematics 010102 general mathematics Torus 01 natural sciences Injective function 010101 applied mathematics symbols.namesake Compact space symbols Observability 0101 mathematics Lebesgue covering dimension Expansive Mathematics
Zdroj:	Journal of the London Mathematical Society. 98:501-516
ISSN:	0024-6107
DOI:	10.1112/jlms.12134
Popis:	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.
Databáze:	OpenAIRE
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