Shadowing and Error Control

How it works

Highlighted claims

• Integer-faithful approximation requires smooth maps to stay within less than one half of the correct integer successor on integer states. — Primitive Recursion without Composition: Dynamical Characterizations, from Neural Networks to Polynomial ODEs
• A discrete Grönwall shadowing lemma controls accumulated error for perturbed maps under a tube condition. — Primitive Recursion without Composition: Dynamical Characterizations, from Neural Networks to Polynomial ODEs
• Decoded shadowing recovers exact integer orbits by rounding approximate states. — Primitive Recursion without Composition: Dynamical Characterizations, from Neural Networks to Polynomial ODEs
• The robust ODE construction keeps sampled states within the decoding basin by choosing a sufficiently large contraction rate. — Primitive Recursion without Composition: Dynamical Characterizations, from Neural Networks to Polynomial ODEs