Are there such continuous chaotic systems, for which an explicit solution exists, which would allow to practically compute state at any given position in time just knowing the initial conditions? Or are they all the explicit solutions limited by the similar drawbacks as Sundman's solution of 3 body problem (extremely slow convergence of series in this case)?
2026-03-27 21:15:47.1774646147
Are there chaotic systems with explicit solutions?
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The abstract of Ramahi and Seydou, A closed form solution of the Helmholtz equation for a class of chaotic resonators, Antennas and Propagation Society International Symposium, 2004. IEEE (Volume:4 ), says,
We study numerically the solution of the Helmholtz equation in a classically chaotic two-dimensional region in the shape of a bow-tie. The quantum ergodicity of classically chaotic systems has been studied extensively, both theoretically and experimentally, in mathematics and in physics. Despite this long tradition, we are able to present a new rigorous result using only elementary calculus. In particular, a closed form solution is derived by using multipole expansions. Our results have been validated by an integral equation method based on layer potential which is solved via the Nyström discretization method.