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We show that the existence of the complete set of guiding functions guarantees the existence of periodic isolating segment that carries the same information concerning periodic solutions of the non-autonomous periodic equations x′=f(x,t).
We develop a geometric approach to problems concerning the existence of T-periodic solutions of a non-autonomous time-T periodic ordinary differential equation. We consider isolating segments, subsets of the extended phase space of the equation, which in some ways resemble isolating blocks from the theory of isolated invariant sets. The union of several contiguous isolating segments is called an isolating...
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