| Popis: |
Consider the following Pfaffian system $$\eqalign{ & d{x_1} = q_1^{(1)}(t,x,u)d{t_1} + ... + q_1^{(m)}(t,x,u)d{t_m}; \cr & \ldots \ldots \ldots \cr & d{x_k} = q_k^{(1)}(t,x,u)d{t_1} + .... + q_k^{(m)}(t,x,u)d{t_m}, \cr} $$ (7.1) where coefficients \(q_i^{(j)}(t,x,u),i = \overline {1,k} ,j = \overline {1,m} ,\) are functions of a vector \(x = \left\| {{x_1},\; \ldots ,\;{x_k}} \right\|\) of dependent variables, vector \(t = \left\| {{t_1},\; \ldots ,\;{t_m}} \right\|\) of independent variables, and vector \(u = \left\| {{u_1},\; \ldots ,\;{u_h}} \right\|\) of parametric variables. The functions \(q_i^{\left( j \right)}\left( {t,x,u} \right)\) are analytical in the domain \(G,G = {R^m} \times {R^k} \times {R^h}.\) |
