$p$-adic discrete dynamical systems and their applications in physics and cognitive sciences

Details $p$-adic discrete dynamical systems and their applications in physics and cognitive sciences $p$-adic discrete dynamical systems and their applications in physics and cognitive sciences

2004-02-23

arxiv.org/abs/nlin/0402042v1

Russian Journal of Mathematical Physics, v.11, N. 1, p.45-70, 2004

Nonlinear Sciences

Adaptation and Self-Organizing Systems

Scientific paper

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.

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