The phase space trajectories of an autonomous system of equations do not intersect, which is a fundamental property of such systems. This can be mathematically proven using the uniqueness theorem for ordinary differential equations, which states that if two trajectories were to intersect, they would represent the same state at that point in time, leading to a contradiction. The physical significance of non-intersecting trajectories indicates that a system's future state is uniquely determined by its initial conditions, ensuring predictability in dynamical systems.
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geet89 said:The phase space trajectories of an autonomous system of equations don't intersect.
Can this be proved mathematically.
Also what is the physical significance of this statement. What happens if they intersect?