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

TL;DR

This review explores $p$-adic discrete dynamical systems, their mathematical properties, and diverse applications in physics and cognitive sciences, highlighting recent developments and interdisciplinary connections.

Contribution

It provides a comprehensive overview of $p$-adic discrete dynamical systems and their applications in physics and psychology, emphasizing new insights into their behavior and utility.

Findings

Analysis of ergodicity and cycle behavior in $p$-adic maps

Applications of $p$-adic dynamics to cognitive science models

Connections between $p$-adic dynamics and physical theories

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.