Abstract
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.
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In the meantime between the workshop and the publication of these proceedings, that conjecture has been proved.
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© 1982 Springer-Verlag
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Bel, L. (1982). Spontaneous predictivisation. In: Llosa, J. (eds) Relativistic Action at a Distance: Classical and Quantum Aspects. Lecture Notes in Physics, vol 162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-11573-0_3
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DOI: https://doi.org/10.1007/3-540-11573-0_3
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