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

Abstract

The aim of this paper is to show that there are no piecewise linear maps of type 2 ∞ 2^{\infty } . For this purpose we use the fact that any piecewise monotone map of type 2 ∞ 2^{\infty } has an infinite ω \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.