Periodic orbits are sequences of points in a dynamical system that repeat after a certain period, meaning that if you iterate a complex function starting from a specific point, you will return to that point after a fixed number of iterations. In the context of complex dynamics and iteration of complex functions, periodic orbits signify stability and are crucial for understanding the behavior of points under repeated application of these functions. They play a key role in the formation of fractals, as the structures generated by such functions often exhibit patterns based on periodic behavior.
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