Geodesic
Gene Expression from 2-adic Dynamical Systems
Informatics and Automation, Selected topics of mathematical physics and $p$-adic analysis, Tome 265 (2009), pp. 142-150

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We perform geometrization of genetics by representing genetic information by points of the 4-adic information space. By a well-known theorem of number theory this space can also be represented as the 2-adic space. The process of DNA reproduction is described by the action of a 4-adic (or equivalently 2-adic) dynamical system. As we know, the genes contain information for production of proteins. The genetic code is a degenerate map of codons to proteins. We model this map as the functioning of a polynomial dynamical system. The purely mathematical problem under consideration is to find a dynamical system reproducing the degenerate structure of the genetic code. We present one of possible solutions of this problem. 
@article{TRSPY_2009_265_a10,
     author = {A. Yu. Khrennikov},
     title = {Gene {Expression} from 2-adic {Dynamical} {Systems}},
     journal = {Informatics and Automation},
     pages = {142--150},
     publisher = {mathdoc},
     volume = {265},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2009_265_a10/}
}
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A. Yu. Khrennikov. Gene Expression from 2-adic Dynamical Systems. Informatics and Automation, Selected topics of mathematical physics and $p$-adic analysis, Tome 265 (2009), pp. 142-150. http://geodesic.mathdoc.fr/item/TRSPY_2009_265_a10/