resonance

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Number Theory and the Arithmetic of Recurrence Number Theory and the Arithmetic of Recurrence
26 min read Keywords:  number theory, KAM, Diophantine approximation, continued fractions, resonance, invariant tori

Once a rule repeats in time, integers appear. Recurrence, resonance, continued fractions, and KAM theory show how arithmetic decides which motions are stable and which fall apart.