FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 2, PAGES 617-620

Periodic trajectories in a Denjoy counterexample

L. K. Bakalinsky

Abstract

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It is shown that for the parametric class of piecewise linear maps
$$
f(x)=
\begin{cases}
\max (k_1x+1,w), & x<0,\\
\min (k_2x-1,w), & x \geq 0
\end{cases}
$$
 ($k_1$ and $k_2$ are greater than one) the range of the parameter $w$, where iterations $x_{n+1}=f(x_n)$ are nonperiodic, has zero Lebesgue measure.

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Last modified: September 1, 2000