Scale free SL(2,R) analysis and the Picard's existence and uniqueness theorem

Details Scale free SL(2,R) analysis and the Picard's existence and uniqueness theorem Scale free SL(2,R) analysis and the Picard's existence and uniqueness theorem

2010-01-11

arxiv.org/abs/1001.1703v1

Int. J. Pure and Applied Math. vol 19, 115-127, (2005)

Mathematics

Classical Analysis and ODEs

Latex 2e, 12 pages

Scientific paper

The existence of higher derivative discontinuous solutions to a first order ordinary differential equation is shown to reveal a nonlinear SL(2,R) structure of analysis in the sense that a real variable $t$ can now accomplish changes not only by linear translations $t \to t + h$ but also by inversions $t \to 1/t$. We show that the real number set has the structure of a positive Lebesgue measure Cantor set. We also present an extension of the Picard's theorem in this new light.

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