In the first section of this paper we define the concept of an Attractor of a hereditary first order differential equation as an ordinary differential equation whose solutions are solutions of the hereditary one and can be interpreted as the asymptotes of its generic solutions. We define also the concept of Predictive Differential Equations associated with a class of hereditary ones depending on a coupling constant G as a first order differential equation which is such that all its solutions are solutions of the corresponding hereditary one and which is analytic in the neighbourhood of G = 0. We report some numerical work proving that for some hereditary equations the corresponding predictive ones are Attractors.
In the second section we consider the retarded electromagnetic equations of two point charges and we prove numerically in a particular case that the associate Predictive Poincaré Invariant System defined in previous papers is an Attractor in an obviously generalized sense. Roughly speaking this means that the retarded electromagnetic equations of motion have a built-in mechanism which causes a spontaneous predictivisation of the causal interaction.
KeywordsPhysical Review Order Differential Equation World Line Causal Interaction Neutral Type
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- 1).R. Bellman and K.L. Cooke. Differential-Difference Equations. Academic Press, 1963Google Scholar
- 2).L.E. El'sgol'ts and S.B. Norkin. Introduction to the Theory and Application of Differential Equations with Deviating Arguments. Academic Press, 1973.Google Scholar
- 3).R.D. Driver. Ordinary and Delay Differential Equations. Springer-Verlag, 1977.Google Scholar
- 4).L. Landau and E. Lifshitz. The Classical Theory of Fields. Addison-Wesley Press, 1951.Google Scholar
- 6).J.L. Sanz. Tesis Universided Autónoma de Madrid (1976).Google Scholar
- 8).L. Bel and X. Fustero. Annales de l'Intitut H. Poincaré 25,411 (1976).Google Scholar
- 9).M. Portilla. Journal of Physics A, 12,1075 (1979).Google Scholar
- 10).L. Bel, Th. Damour, N. Deruelle, J. Ibañez and J. Martin. To be published in General Relativity and Gravitation.Google Scholar
- 13).L. Bel. Annales de l'Institut H. Poincaré, 12,307 (1970).Google Scholar
- 14).L. Bel. Lecciones de Mecánica Relativista Predictive. Universidad Autónoma de Barcelona (1976).Google Scholar
- 15).L. Bel and J. Martin. Annales de l'Institut H. Poincaré, 33,409 (1980).Google Scholar
- 16).Droz-Vincent. Physica Scripta 2,129 (1970).Google Scholar
- 18).A. Salas and J.M. Sánchez-Rón. Il Nuovo Cimento 20B,209 (1974).Google Scholar
- 19).L. Bel. Journées Relativistes de Toulouse, Université de Toulouse (1974).Google Scholar
- 21).J.C. Kasher and S.L. Schwebel. Physical Review D4,2956 (1971)Google Scholar
- 22).C.M. Andersen and Hans C. von Bayer. Physical Review D5,2470 (1972).Google Scholar
- 23).J. Huschilt, W.E. Baylis, D. Leiter and G. Szamosi. Physical Review D7,2844 (1973).Google Scholar
- 24).J. Huschilt and W.E. Baylis. Physical Review D13,3256 (1976).Google Scholar
- 25).W.E. Baylis and J. Huschilt. Physical Review D13,3262 (1976).Google Scholar
- 26).In the meantime between the workshop and the publication of these proceedings, that conjecture has been proved.Google Scholar