This allows us to simplify the arguments in the notation for solutions of autonomous vector fields, i.e., \(x(t, 0, x_{0}) \equiv x(t, x_{0})\) with \(x(0, 0, x_{0}) = x(0, x_{0}) = x_{0}\). We often ...This allows us to simplify the arguments in the notation for solutions of autonomous vector fields, i.e., \(x(t, 0, x_{0}) \equiv x(t, x_{0})\) with \(x(0, 0, x_{0}) = x(0, x_{0}) = x_{0}\). We often use the phrase ''the flow generated by the (autonomous) vector field''. Autonomous is in parentheses as it is understood that when we are considering flows then we are considering the solutions of autonomous vector fields.
