Nonlinear Dynamics

, Volume 50, Issue 1–2, pp 191–211 | Cite as

Reynolds’ dream?

  • Jerzy Hańćkowiak
Original Article


For many non-linear phenomena, it is necessary to solve infinite systems of equations for correlation functions with a wide range of parameters. This paper can be seen as a first step in addressing this problem. Correlation functions related to the ϕ3 and to the ϕ4 field theories are described by means of generating Fock space vectors constructed with the help of Cuntz algebra. The equations obtained are easily transformed and general solutions are constructed. Various expansions of these solutions are developed using the explicitly constructed right inverse operators related to linear and non-linear parts of the theory. Based on the idea of information loss and using the language of classical mechanics, a solution to the closure problem for correlation functions is proposed. The method described in this paper can be used to obtain approximated correlation functions with strong and weak non-linearity.


Closure problem Cuntz relations Ideal constraints D’Alembert principle 


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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of Zielona Góra. ul. Podgórna 50Zielona GóraPoland

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