P-adic Deterministic and Random Dynamics - Khrennikov, Andrei Yu (Springer Netherlands, 2004)
?eldK(and,forexample,p-adicsuperspaces). LateronI.V.Volovichproposed the ?rst model ofp-adic string, see Chapter 1. We also remark that the non-Archimedean theory of dynamical systems is a very natural ?eld for applications of non-Archimedean analysis—analysis for mapsf : K? K, see Chapter 1. In 1997, see [101], A. Yu. Khrennikov proposed to applyp-adic dynamical systemsformodelingofcognitiveprocesses. Inapplicationsofp-adicnumbers to cognitive science the crucial role is played not by the algebraic structure of Q , but by its tree-like hierarchical structure. This structure of a p-adic tree p is used for a hierarchical coding of mental information and the parameter p characterizesthecodingsystemofacognitivesystem. Therefore,insuchp-adic cognitive models the assumption thatp is a prime number is not so natural. We can apply dynamical systems in rings ofp-adic numbersQ , wherep> 1 is an p arbitrarynaturalnumber. Foundationsofp-adiccognitivemodelsarepresented in detail in the book [111], see also Chapter 8, Chapter 11, and Chapter 12 for new developments of this theory. ThisbookismainlybasedontheresultsofinvestigationsoftheVaxj ¨ og ¨ roupin p-adic dynamical systems: Professor Andrei Yu. Khrennikov and the graduate students Karl-Olof Lindahl, Marcus Nilsson, Robert Nyqvist, and Per-Anders Svensson. One of the main streams in the research of the V¨ axj¨ o group was induced by an observation, see [101], that in the theory ofp-adic dynamical systems there appearsa new important parameter - the prime numberp giving the basis of the corresponding number ?eld Q . Therefore it may be interesting to investigate p dependence of some characteristics of a dynamical system on p, especially whenp??
Keywords: Mathematics; Geometry, algebraic; Field theory (Physics); Functional analysis; Mathematical physics; Consciousness; Field Theory and Polynomials; Mathematical Methods in Physics; Cognitive Psychology; Functional Analysis; Algebraic Geometry; Mathematik; Mathematische Physik; Differenzierbares dynamisches System; p-adische Analysis