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Entropy 2016, 18(5), 160; doi:10.3390/e18050160

Fractal Information by Means of Harmonic Mappings and Some Physical Implications

1
Department of Physics, Gheorghe Asachi Technical University of Iaşi, Iaşi 700506, Romania
2
Faculty of Mathematics, Alexandru Ioan Cuza (Al.I. Cuza) University, Iaşi 700506, Romania
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Department of Physics, Faculty of Applied Sciences, Politehnica University of Bucharest, Bucharest 060042, Romania
4
Economic and Marketing Department, Technical University Gheorghe Asachi from Iaşi, Iaşi 700050, Romania
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Faculty of Physics, Alexandru Ioan Cuza (Al.I. Cuza) University, Iaşi 700506, Romania
6
Faculty of Engineering, University ”Vasile Alecsandri” of Bacău, Bacău 600115, Romania
*
Author to whom correspondence should be addressed.
Academic Editor: Carlo Cattani
Received: 25 March 2016 / Revised: 16 April 2016 / Accepted: 20 April 2016 / Published: 26 April 2016
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory II)
View Full-Text   |   Download PDF [320 KB, uploaded 26 April 2016]

Abstract

Considering that the motions of the complex system structural units take place on continuous, but non-differentiable curves, in the frame of the extended scale relativity model (in its Schrödinger-type variant), it is proven that the imaginary part of a scalar potential of velocities can be correlated with the fractal information and, implicitly, with a tensor of “tensions”, which is fundamental in the construction of the constitutive laws of material. In this way, a specific differential geometry based on a Poincaré-type metric of the Lobachevsky plane (which is invariant to the homographic group of transformations) and also a specific variational principle (whose field equations represent an harmonic map from the usual space into the Lobachevsky plane) are generated. Moreover, fractal information (which is made explicit at any scale resolution) is produced, so that the field variables define a gravitational field. This latter situation is specific to a variational principle in the sense of Matzner–Misner and to certain Ernst-type field equations, the fractal information being contained in the material structure and, thus, in its own space associated with it. View Full-Text
Keywords: fractal information; fractal entropy; variational principle; mapping; economy; econometrics; management; economic statistics fractal information; fractal entropy; variational principle; mapping; economy; econometrics; management; economic statistics
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Agop, M.; Gavriluţ, A.; Păun, V.P.; Filipeanu, D.; Luca, F.A.; Grecea, C.; Topliceanu, L. Fractal Information by Means of Harmonic Mappings and Some Physical Implications. Entropy 2016, 18, 160.

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