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Can there be a situation, where the time dilation is oscillating, in the sense that one observer notes that the time for the other frame is moving faster then slower, etc...? Can this oscillation be very high? I know it maybe a not very precise question, but any help would be appreciated.

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Yes, when the velocity of the other frame is oscillating. I.e., the other frame must be accelerating back and forth. However, the observer will never see time in the other frame going faster than in his own. It always goes slower, though the relative amount of "slowness" varies depending on the relative velocity. – Michael Brown Jan 21 at 0:29
Unless you have gravity (the question is tagged general-relativity, after all), then it can go faster. – Retarded Potential Jan 21 at 6:40

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