  This paper presents analyses for the maximum hands-off control using the
geometric methods developed for the theory of turnpike in optimal control.
First, a sufficient condition is proved for the existence of the maximum
hands-off control for linear time-invariant systems with arbitrarily fixed
initial and terminal points using the relation with $L^1$ optimal control.
Next, a sufficient condition is derived for the maximum hands-off control to
have the turnpike property, which may be useful for approximate design of the
control.

Optimization and Control