Norton's dome: a Newtonian surface where determinism fails at the Lipschitz-singular apex
Norton’s dome is a surface with shape h = (2/3g)*r^(3/2), where a ball placed at rest at the apex has infinitely many solutions to Newton’s second law: it can remain at rest forever, or spontaneously begin sliding down at any arbitrary future time. This non-uniqueness arises because the equation of motion fails the Lipschitz condition at the apex, violating the hypotheses of the Picard-Lindelof existence and uniqueness theorem.
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