Abstract
The world is a partial differential equation (P.D.E.) — to some approximation at. least. The qualitative behavior of P.D.E.s, however, is potentially infinitely complex. It is therefore fortunate that some P.D.E.s behave precisely like ordinary differential equations (O.D.E.s) in some of their regimes. Two recent cases in point are the surprising discovery of silent turbulence by DALLMANN [1], and the successful analytic demonstration of constant-shape traveling chaotic waves in a boundary value problem of reaction-diffusion type, RÖSSLER & KAHLERT [2]. A third example is the new observation by SREENIVASAN [3] that turbulent vortex streets involve, with comparable probabilities, either hypertori of up to 50 dimensions or related hyperchaos of the same dimensionality (cf. RÖSSLER [4] for these notions).
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Rössler, O.E., Kahlert, C., Uehleke, B. (1985). Tori and Chaos in a Simple C1-System. In: Jordan, H.L., Oertel, H., Robert, K. (eds) Nonlinear Dynamics of Transcritical Flows. Lecture Notes in Engineering, vol 13. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82506-4_3
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DOI: https://doi.org/10.1007/978-3-642-82506-4_3
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