The Differential Equations of Dynamics ... |
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9 Xn analogous approximations P(p B₁ BENDIXSON canonical closed interval closed set considered continuous functions continuous partial derivatives converge uniformly corresponding derivatives with respect determinant differential equations dx dt equations 12 exact solution existence holomorphic with respect homogeneous linear equations increments inequalities 19 infinite sequence infinite series initial conditions initial constants initial values interior points intervals less Jacobians LEMMA less than I(7 limit-point LINDELÖF Math Méth method of variation moduli neighborhood normal integrals Nouv PAINLEVÉ partial derivatives periodic solution PICARD POINCARE point N₁ positive numbers Pr(t preceding theorems real variables realm D respect to x₁ second members set R(e single-valued functions solution P(t solutions as functions solutions of equations t=to t₁ tions tj+1 transformations of variables uniformly convergent series uniquely defined upper bound independent variation of parameters w₁ αξι Οσ Σ Σ ΣΧ др