  We consider dynamics of a scalar piecewise linear "saw map" with infinitely
many linear segments. In particular, such maps are generated as a Poincar\'e
map of simple two-dimensional discrete time piecewise linear systems involving
a saturation function. Alternatively, these systems can be viewed as a feedback
loop with the so-called stop hysteresis operator. We analyze chaotic sets and
attractors of the "saw map" depending on its parameters.

Dynamical Systems