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Saying a point $p$ is fixed by $f^m$ means that applying the function $f$ exactly $m$ times to $p$ returns $p$ itself. This rephrases the definition of a periodic point of period $m$ as a fixed point of the $m$-fold iterate of $f$.

Conditions: $f$ is a function.; $m$ is a positive integer.; $p$ is a point in the domain of $f$.

Saying a point $p$ is fixed by $f^m$ means that applying the function $f$ exactly $m$ times to $p$ returns $p$ itself. This rephrases the definition of a periodic point of period $m$ as a fixed point of the $m$-fold iterate of $f$.

Conditions: $f$ is a function.; $m$ is a positive integer.; $p$ is a point in the domain of $f$.

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.