In the proof of Chataev's instability theorem, it is assumed that there exists an $m>0$ such that m is the minimum value of the change in the Lyapunov function $V$ with time for the given positive orbit. Why is this the case? Is it not possible to have an orbit where $V^\prime$ decreases monotonically with the limit $0$?
2026-03-25 22:06:09.1774476369
Why does the change of the Lyapunov function with time of a particular orbit necessarily have a minimum value in Chataev's instability theorem?
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