Chaotic systems exhibit sensitive dependence on initial conditions, meaning any finite specification of initial state—however precise—diverges exponentially from the true trajectory.

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Chaotic systems(as used in mathematics and physics): Systems that appear random and unpredictable even though they follow fixed rules, because they're so sensitive to starting conditions.
Diverges exponentially(as used in mathematics and systems behavior): Moves apart at an increasingly rapid rate, where the gap grows faster and faster rather than staying constant or growing slowly.
Finite specification(as used in epistemology and measurement): A description of something that has limits or boundaries—in this case, measuring initial conditions with only a limited amount of precision, not perfect precision.
Sensitive dependence on initial conditions(as used in chaos theory and predictability discussions): The idea that even microscopic differences in how a system starts will eventually produce wildly different results—like how a butterfly's wing flap could theoretically trigger a chain of events leading to a hurricane.

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