Stability and expansivity of tent map

Carrasco-Olivera, D.; Morales, C.; Villavicencio, H.

doi:10.1090/proc/15244

Stability and expansivity of tent map
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by D. Carrasco-Olivera, C. A. Morales and H. Villavicencio PDF

Proc. Amer. Math. Soc. 149 (2021), 773-786 Request permission

Abstract:

We discuss the stability and the expansivity of the tent map $f:[0,1]\to [0,1]$ defined by $f(x)=2\min \{x,1-x\}$ for $0\leq x\leq 1$. Indeed, we show that $f$ is neither topologically stable nor orbit shift topologically stable nor countably-expansive but is cw-topologically stable, orbit shift cw-expansive, and orbit shift $\alpha$-persistent.

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