  Every oriented closed geodesic on the modular surface has a canonically
associated knot in its unit tangent bundle coming from the periodic orbit of
the geodesic flow. We study the volume of the associated knot complement with
respect to its unique complete hyperbolic metric. We show that there exist
sequences of closed geodesics for which this volume is bounded linearly in
terms of the period of the geodesic's continued fraction expansion.
Consequently, we give a volume's upper bound for some sequences of Lorenz knots
complements, linearly in terms of the corresponding braid index. Also, for any
punctured hyperbolic surface we give volume's bounds for the canonical lift
complement relative to some sequences of sets of closed geodesics in terms of
the geodesics length.
