LLSLS G 0SGGGGS0SGYSGGGS0S0S0S Academic Article uri icon

abstract

  • J is a diagonal matrix (or in Jordan form) having eigenvalues with zero real parts and G (a) is a set of strictly nonlinear functions of a. The solution (1.3) and the amplitude equations (14) are derived simultaneously in a perturbative manner to the prescribed order in the amplitudes o. It is evident from Eq.(1.3) that the time dependence of the solution U is determined by that of the critical amplitudes a,(or GGS This is a manifestation of the center- manifold theorem which proves the existence of an invariant manifold f,(a)(cf. Sec. V). The amplitudes a in turn satisfy amplitude equations (Eq.(14) whose nonlinear part G (a) has a nor-mal form (ie, contains the least number of nonlinear terms). This form is achieved by means of a nonlinear transformation which is applied implicitly to the original amplitudes a" and whose inverse is given by Eq.(1.5)(cf. Sec. VI), The paper is organized as follows. In …

publication date

  • January 1, 1986