Asymptotic linear - nonlinear duality, indeterminism and mathematical intelligence

The formalism of asymptotic duality structure with applications to late time asymptotic states of linear and nonlinear systems is presented. A scale invariant linear differential system is shown to admit higher derivative discontinuous, nonsmooth solutions under the action of asymptotic duality transformations. The relevant asymptotic quantities are self dual and finitely differentiable. The geometrical meaning and applications to higher order nonlinear systems are presented on the space of differentiable functions. A novel duality relationship between linear and nonlinear systems is exposed. A linear system is shown to extend self similarly over nonlinear, classically inaccessible scales thereby extending classical smooth solution space to a nonsmooth one. A nonlinear system, on the other hand, is shown to proliferate into a system of self similar linear equations that could be solved exactly to have a very efficient high precision computation of periodic orbits. An extension of self dual asymptotics to critically self dual case in the space of continuous functions reveals a connection to prime number theorem and the associated correction term respecting the Riemann hypothesis.