Shadowing and Error Control
Integer-faithful approximation requires smooth maps to stay within less than one half of the correct integer successor on integer states. A discrete Grönwall shadowing lemma controls accumulated error for perturbed maps under a tube condit…
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Integer-faithful approximation requires smooth maps to stay within less than one half of the correct integer successor on integer states. A discrete Grönwall shadowing lemma controls accumulated error for perturbed maps under a tube condition. Decoded shadowing recovers exact integer orbits by rounding approximate states. The robust ODE construction keeps sampled states within the decoding basin by choosing a sufficiently large contraction rate.