Duality Structure, Asymptotic analysis and Emergent Fractal sets
Abstract
A new, extended nonlinear framework of the ordinary real analysis incorporating a novel concept of {\em duality structure} and its applications into various nonlinear dynamical problems is presented. The duality structure is an asymptotic property that should affect the late time asymptotic behaviour of a nonlinear dynamical system in a nontrivial way leading naturally to signatures generic to a complex system. We argue that the present formalism would offer a natural framework to understand the abundance of complex systems in natural, biological, financial and related problems. We show that the power law attenuation of a dispersive, lossy wave equation, conventionally deduced from fractional calculus techniques, could actually arise from the present asymptotic duality structure. Differentiability on a Cantor type fractal set is also formulated.
Cite
@article{arxiv.1602.01486,
title = {Duality Structure, Asymptotic analysis and Emergent Fractal sets},
author = {Dhurjati Prasad Datta and Soma Sarkar},
journal= {arXiv preprint arXiv:1602.01486},
year = {2019}
}
Comments
This is published version of the original preprint "Duality Structure, Nonarchimedean Extension of the Real Number System and Emergent Fractals", No. of pages:32. Also removed most of the unfortunate Latex/Macro definition errors of the published paper