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I have asked this question at math.stackexchange, but I have been redirected here.

My question is, if there is any historical relation between the fields of Dynamical systems (and related fields such as Optimal control) and (theoretical) Computer science. The reason for which I ask this question is, that several older major journals, now considered to be primarily focused on theoretical computer science, were originally devoted both to computer science and to dynamical systems.

The example of such journals can be for instance Journal of Computer and System Sciences. Mainly in its beginnings (however, I am too young to remember these times), it published papers both on computer science and on system sciences, and both of the fields seemed to be of equal importance. Moreover, also the name of the journal Information and Control suggests the relation to optimal control. However, this journal was always focused mainly on theoretical computer science and information theory.

So therefore I wonder, if these fields (nowadays, up to my knowledge, considered to be substantially different) have something in common or if there is some purpose to consider these fields to be related.

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  • $\begingroup$ At a random guess, the connection was simply that dynamical systems and related fields were areas of math where computing was obviously necessary to tackle interesting problems. So people working in those areas were interested in computer science, and a computer scientist looking for an interesting challenge to set a computer to could naturally be lead to look at those fields. $\endgroup$ – btilly Jul 7 '12 at 1:20
  • $\begingroup$ The focus of any given journal may shift for a variety of reasons. Do you have more evidence of a strong connection? $\endgroup$ – Raphael Jul 9 '12 at 8:49
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Yes there did seem to be historically a strong connection between study of dynamical systems and advanced theoretical computer science, that is shifted dramatically over time. Some of this has become mainstream and incorporated into more "core CS" (for example the empirical study of algorithms running on the SAT transition point and their strong thermodynamic/physics analogies, or empirically studied behavior of differential equations too difficult to solve exactly, etc) and some of it has moved into separate areas of more "applied" research, eg simulations of complex systems. Here are some refs on the history that might be helpful:

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  • $\begingroup$ addendum. its a very subtle and nuanced question about the way that "complexity theory" historically overlaps with "computational complexity theory" and how the two continue to crosspollinate. the former is newer. see also wikipedia complex adaptive system. one area of particular overlap is with cellular automata, eg Wolfram. another is with fractals. another way to approach this is to note researchers who have worked in or made major contributions to both fields. it becomes difficult/blurry to discriminate the two sharply at times. $\endgroup$ – vzn Sep 10 '12 at 18:11
  • $\begingroup$ see also complex systems, wikipedia with a good graphical timeline $\endgroup$ – vzn Sep 10 '12 at 18:17

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