Andriy P. KYRYLYUK  (= Andrei P. KIRILYUK)
Solid State Theory Department,
Institute of Metal Physics of NAS of Ukraine,
Prospect Vernadskogo 36,
Kyiv, 03142 UKRAINE

Universal symmetry of complexity and its manifestations at different levels of world dynamics

A universally nonperturbative analysis of an arbitrary interaction process described by a quite general dynamical equation provides the 'dynamically multivalued' general solution that contains many equally valid, locally complete problem solutions representing possible system configurations, or 'realisations'. This unreduced solution leads to purely dynamical, rigorously derived (nonaxiomatic) definitons of true randomness, probability, chaoticity, complexity, nonlinearity and other related properties [1, 2] which extend considerably their axiomatic introduction in the conventional, dynamically single-valued theory ('exact solutions' and their 'small perturbations'). Any dynamical system evolution can now be expressed in terms of the absolutely universal law of conservation, or symmetry, of complexity that includes extended, universally applicable versions of the 'first' and 'second' laws of thermodynamics (conservation and degradation of energy, respectively) and actually any other (correct) dynamical symmetry, law, or 'principle', governing real system development. We demonstrate particular manifestations of this universal symmetry at various levels of world dynamics [1, 2], including causally complete, intrinsically unified explanation of 'quantum mysteries' and 'relativistic' effects [3], purely dynamic origin of (true) quantum and classical chaos related by the ordinary correspondence principle [4], extended, dynamically probabilistic fractals and their applications in biology and medicine [5].


  1. A.P. Kirilyuk, "Universal Concept of Complexity by the Dynamic Redundance Paradigm: Causal Randomness, Complete Wave Mechanics, and the Ultimate Unification of Knowledge" (Naukova Dumka, Kiev, 1997), 550 p., in English. For a non-technical review see also physics/9806002
  2. A.P. Kirilyuk, "Dynamically Multivalued, Not Unitary or Stochastic, Operation of Real Quantum, Classical and Hybrid Micro-Machines", physics/0211071
  3. A.P. Kirilyuk, "Universal gravitation as a complex-dynamical process, renormalised Planckian units, and the spectrum of elementary particles", gr-qc/9906077
  4. A.P. Kirilyuk, "Quantum chaos and fundamental multivaluedness of dynamical functions", Annales de la Fondation Louis de Broglie, v. 21 (1996) 455; quant-ph/9511034
  5. A.P. Kirilyuk, "The Universal Dynamic Complexity as Extended Dynamic Fractality: Causally Complete Understanding of Living Systems Emergence and Operation", In: "Fractals in Biology and Medicine", Vol. III, ed. by G.A. Losa, D. Merlini, T.F. Nonnenmacher, and E.R. Weibel (Birkh?user, Basel, 2002), p. 271.