Positive top Lyapunov exponent via invariant cones: Single trajectories

We establish criteria for the positivity of the top Lyapunov exponent of a nonautonomous dynamics in terms of invariant cone families, both for maps and flows. The families of cones are associated with quadratic forms of type (k,p−k)(k,p−k) with k arbitrary. Our work can be seen as a counterpart of results in the context of ergodic theory, where the positivity of the top Lyapunov exponent is obtained for almost all trajectories although saying nothing about each specific trajectory.