{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:19:14Z","timestamp":1760242754505,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2016,4,26]],"date-time":"2016-04-26T00:00:00Z","timestamp":1461628800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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 Schr\u00f6dinger-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 \u201ctensions\u201d, which is fundamental in the construction of the constitutive laws of material. In this way, a specific differential geometry based on a Poincar\u00e9-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\u2013Misner 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.<\/jats:p>","DOI":"10.3390\/e18050160","type":"journal-article","created":{"date-parts":[[2016,4,26]],"date-time":"2016-04-26T10:21:21Z","timestamp":1461666081000},"page":"160","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Fractal Information by Means of Harmonic Mappings and Some Physical Implications"],"prefix":"10.3390","volume":"18","author":[{"given":"Maricel","family":"Agop","sequence":"first","affiliation":[{"name":"Department of Physics, Gheorghe Asachi Technical University of Ia\u015fi, Ia\u015fi 700506, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alina","family":"Gavrilu\u0163","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics, Alexandru Ioan Cuza (Al.I. Cuza) University, Ia\u015fi 700506, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Viorel","family":"P\u0103un","sequence":"additional","affiliation":[{"name":"Department of Physics, Faculty of Applied Sciences, Politehnica University of Bucharest, Bucharest 060042, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dumitru","family":"Filipeanu","sequence":"additional","affiliation":[{"name":"Economic and Marketing Department, Technical University Gheorghe Asachi from Ia\u015fi, Ia\u015fi 700050, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Florin","family":"Luca","sequence":"additional","affiliation":[{"name":"Economic and Marketing Department, Technical University Gheorghe Asachi from Ia\u015fi, Ia\u015fi 700050, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Constantin","family":"Grecea","sequence":"additional","affiliation":[{"name":"Faculty of Physics, Alexandru Ioan Cuza (Al.I. Cuza) University, Ia\u015fi 700506, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liliana","family":"Topliceanu","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, University \u201dVasile Alecsandri\u201d of Bac\u0103u, Bac\u0103u 600115, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,4,26]]},"reference":[{"key":"ref_1","unstructured":"Chen, F. (1994). Introduction to Complex System Physics, Springer. [2nd ed.]."},{"key":"ref_2","unstructured":"Morozov, I. (2012). Introduction to Complex System Dynamics, CRC Press."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Dimitriu, D.G., Aflori, M., Ivan, L.M., Ioni\u0163\u0103, C., and Schrittwieser, R.W. (2007). Common physical mechanism for concentric and non-concentric multiple double layers in plasma. Plasma Phys. Control. 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