I am reading through Arnold's "Mathematical Methods Of Classical Mechanics". In the section 4D on p. 21 concerning Phase Flow there is a question that reads as follows:
Show that if Potential Energy is postive, then there is a phase flow. Hint: Use the law of conservation of energy to show that a solution can be extended without bound.
I am stumped. Can somebody give me any other hints?
For context, Arnold defines a phase flow as a one-parameter group of diffeomorphisms of the phase plane to itself (the parameter in question being time so that the position of a point $M$ in the phase plane can be traced for all time $t$).