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I've thought about something related.
In one point of view, time traveling to the past can create paradoxes since it alters events after that moment in the past, which could cause you to never time travel to the past after.
After some thinking, I got the feeling that the fixed-point theorem was connected to this. As long as whatever you do in the past causes you to time travel to the past again and do the same thing in the future, the paradox doesn't happen. What you do when you time travel is like the input, and what you do when you time travel again in the resulting future is like the output.
When the input and output are the same, everything works out.
After searching about this on the internet, I saw other people have thought about and discussed this.