IJPAM: Volume 19, No. 1 (2005)

SCALE FREE SL(2,R) ANALYSIS AND
THE PICARD'S EXISTENCE AND
UNIQUENESS THEOREM

Dhurjati Prasad Datta
Department of Mathematics
North Bengal University
Darjeeling, 734430, INDIA
e-mail:dp_datta@yahoo.com


Abstract.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 $t \rightarrow t + h$ but also by inversions $t \rightarrow 1/t$. 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.

Received: February 2, 2005

AMS Subject Classification: 26E35, 34F05, 46F30

Key Words and Phrases: scale free, Cantor set, infinitesimals, nonlinear analysis

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 19
Issue: 1