自励系の安定性理論 : ベクトル場の流れと自励系常微分方程式

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In this paper, I summarized the stability theories philologicaly on the ordinary differential equations of the autonomous system, and showed them concretely with a exercise of the stability on the Lorenz's model. The motive of this paper is to consider the Chaos phenomena as the behavior of solution curves on the maniforld. These studies started just now, many researchers actively atempt to explain the solution orbits as the knotentheorie or the combinational topology. This paper is equal to a basic stage of above theories, I showed it divided by four steps as follows, (i) The first step is to consider the flow as the integral curve group on the vector field in the maniforld. (ii) The second step ; to consider (i) as the ordinary differential eguations of the autonomous system, and to show the uniqueness and the existence of solution of the above equation. (iii) The third step ; to consider the stability of solution in the neighbourhood of the fixed point as the stability theory of the autonomous system. (iv) The final step ; to consider (iii) as the theory of the central manifold. As a result, I showed a distinct difference between the stability on the differentiable manifold and one on the ordinary differential equation in this paper.
広島文化学園大学の論文
2000-08-31