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

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.

References in corpus (2)

• Application of p-adic analysis to models of spontaneous breaking of the replica symmetry
• Stochastic processes on non-Archimedean spaces with values in non-Archimedean fields

Cited by in corpus (8)

• $q$-Bernoulli Numbers and Polynomials Associated with Multiple $q$-Zeta Functions and Basic $L$-series
• Replica symmetry breaking related to a general ultrametric space I: replica matrices and functionals
• Replica symmetry breaking related to a general ultrametric space III: the case of general measure
• Replica symmetry breaking related to a general ultrametric space II: RSB solutions and the n\to0 limit
• Ultrametric pseudodifferential operators and wavelets for the case of non homogeneous measure
• Non-Archimedean Replicator Dynamics and Eigen's Paradox
• Estimates of linearization discs in $p$-adic dynamics with application to ergodicity
• Ultrametric random field