Higher derivative discontinuous solutions to linear ordinary differential equations: A new route to complexity?

Details Higher derivative discontinuous solutions to linear ordinary differential equations: A new route to complexity? Higher derivative discontinuous solutions to linear ordinary differential equations: A new route to complexity?

2010-01-10

arxiv.org/abs/1001.1499v1

Chaos, Solitons and Fractals, vol 22, issue 2, (2004), 271-275

Mathematics

General Mathematics

AMS-latex 2e, 6 pages, no figure

Scientific paper

We present a new one parameter family of second derivative discontinuous solutions to the simplest scale invariant linear ordinary differential equation. We also point out how the construction could be extended to generate families of higher derivative discontinuous solutions as well. The discontinuity can occur only for a subset of even order derivatives, viz.,2nd, 4th, 8th, 16th, ....The solutions are shown to break the discrete parity (reflection) symmetry of the underlying equation. These results are expected to gain significance in the contemporary search of a new {\em dynamical principle} for understanding complex phenomena in Nature.

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