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$p$-adic discrete dynamical systems and their applications in physics and cognitive sciences | | Andrei Khrennikov
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23 Feb 2004 | | Journal: | Russian Journal of Mathematical Physics, v.11, N. 1, p.45-70, 2004 | | Subject: | Adaptation and Self-Organizing Systems | nlin.AO | | Abstract: | This review is devoted to dynamical systems in fields of $p$-adic numbers: origin of $p$-adic dynamics in $p$-adic theoretical physics (string theory, quantum mechanics and field theory, spin glasses), continuous dynamical systems and discrete dynamical systems. The main attention is paid to discrete dynamical systems - iterations of maps in the field of $p$-adic numbers (or their algebraic extensions): conjugate maps, ergodicity, random dynamical systems, behaviour of cycles, holomorphic dynamics. dynamical systems in finite fields. We also discuss applications of $p$-adic discrete dynamical systems to cognitive sciences and psychology. | | Source: | arXiv, nlin.AO/0402042 | | Services: | Forum | Review | PDF | Favorites | |
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