A general non-Newtonian n-body problem and dynamical scenarios of solutions

[Speaker] Chino, Naohito:1
1:Aichi Gakuin University (Japan)

A general non-Newtonian n-body problem is discussed and various possible dynamical scenarios for solutions to some difference equation models are shown whose state space is either a finite-dimensional complex Hilbert space or an indefinite space. By the problem we mean formation of a group structure and its change over time through interactions among members of a group. These members can be nations, humans, animals, neurons, cells, electrons, and so on, and it is assumed that these interactions are generally asymmetric. In analyzing the dynamical scenarios for solutions we utilize not only methods of linear time series analysis but also those of non-linear (chaotic) time series analysis. We shall show that even a dyadic relation model, which is a special case of our models, includes a Mandelbrot set as a special case. The relation of the formation of a group structure simulated in our models to dissipative structure is discussed.
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