There are no piecewise linear maps of type 2^{∞}

López, Víctor; Snoha, L’ubomír

doi:10.1090/S0002-9947-97-01801-1

There are no piecewise linear maps of type $2^{\infty }$
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by Víctor Jiménez López and L’ubomír Snoha

Trans. Amer. Math. Soc. 349 (1997), 1377-1387

DOI: https://doi.org/10.1090/S0002-9947-97-01801-1

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Abstract:

The aim of this paper is to show that there are no piecewise linear maps of type $2^{\infty }$. For this purpose we use the fact that any piecewise monotone map of type $2^{\infty }$ has an infinite $\omega$-limit set which is a subset of a doubling period solenoid. Then we prove that piecewise linear maps cannot have any doubling period solenoids.

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