Fractal dimension of chaotic dynamical spaces

S.I. Nada

Chaos, Solitons & Fractals, 2006, vol. 30, issue 2, 374-379

Abstract: In his paper [Chaos, Solitons & Fractals 4 (1994) 293–6], E1 Naschie has exposed the existence of sets with dimensions between 0 and −1, which he calls the cantorian sets. E1-Ghoul discussed some problems in fractal dimensions [Chaos, Solitons & Fractals, England 4 (2001) 77–80; Chaos, Solitons & Fractals, England 18 (2003) 187–92]. The present work is intended to extend their works for chaotic dynamical manifolds. This is obviously related to the cantorian geometry with a possible model for quantum mechanics. The folding of these spaces and their relations with dimensions are studied. Special emphasis on ε-dimension, 0<ε≪1 is given and some generalized theorems from classical dimension theory are introduced.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:30:y:2006:i:2:p:374-379

DOI: 10.1016/j.chaos.2005.09.039

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