preprints.org > computer science and mathematics > mathematics > doi: 10.20944/preprints202401.0328.v2

Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 31 December 2023 / Approved: 3 January 2024 / Online: 4 January 2024 (07:11:12 CET)
Version 2 : Received: 5 January 2024 / Approved: 6 January 2024 / Online: 8 January 2024 (06:30:30 CET)

This work presents a new type of chaotic dynamical system originated from Dirichlet Eta function. Although the exposition describes only a bidimensional instance, it is certainly possible to construct higher dimensional such models. The novelty resides in the multitude of interesting characteristics concentrated in only one kind of dynamical system, mainly because of its simple abstract definition - it provokes dissipative, chaotic and itinerant behavior, and its paths typically display nonrecurring quasi-attractors and associate regions of ruin. In addition, it is discrete and nonautonomous, being additively driven by a simple real vector sequence. Also, the defining formulas have parameters which permit to activate bifurcatory effects, mainly related to setting the number of quasi-attractors and overall geometric complexity and diversity. In this fashion, it holds a certain similarity with classical itinerant chaotic systems, but it is a completely different object. One of its parameters is very influential and may be intuitively compared to a type of "potential energy", capable of changing the duration of sojourns etc. In this fashion, there is a potential opportunity to employ artificial inference techniques for designing specific structures on paths. Of course, the other parameters are also relevant, but not necessarily in the control of the number of quasi-attractors and the permanence periods near them. It is important to state that the described system was found during a previous investigation about certain features of the Riemann hypothesis, using the Dirichlet Eta function instead of the Riemann Zeta function - the components of the system under study here were part of certain series whose convergence had to be established, and that scenario produced this very positive side effect. The text also suggests an atypical, but important, potential application in philosophy: the representation of the Hindu concepts of Samsara and Moksha.

Dirichlet Eta function; Samsara; Moksha; Quasi-attractor; Bifurcation; Chaotic Itinerancy

Computer Science and Mathematics, Mathematics

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