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In trigonometry, periodicity describes repetition in the function's graph over its input variable. In this setting, period describes the recurrence of a specific point under repeated iteration of a function.

Conditions: Comparing dynamical systems period with trigonometric period.

In trigonometry, periodicity describes repetition in the function's graph over its input variable. In this setting, period describes the recurrence of a specific point under repeated iteration of a function.

Conditions: Comparing dynamical systems period with trigonometric period.

A periodic point of period $m$ is a point that returns to itself after $m$ iterations of the function. The video emphasizes that this is recurrence under repeated application of $f$, not the same notion of period used for trigonometric functions.

Conditions: $f$ is a function under consideration.; $m$ is a positive integer counting the number of iterations.; $p$ is a point for which the iterates are defined.

A periodic point of period $m$ is a point that returns to itself after $m$ iterations of the function. The video emphasizes that this is recurrence under repeated application of $f$, not the same notion of period used for trigonometric functions.

Conditions: $f$ is a function under consideration.; $m$ is a positive integer counting the number of iterations.; $p$ is a point for which the iterates are defined.