Adiabatic Invariants for a Dyrac System
by
Yeghiazar Taroyan
Institute of mathematics, National Academy of Sciences of Armenia

In the present paper we derive asymptotic solutions for a Dirac system of 2n order without the restriction on the variable matrix of the system to equal zero at infinity. Using these asymptotic solutions we construct adiabatic invariants and estimate their changes. The formulas of these invariants contain differences of elements of the variable matrix in denominators. The smooth are elements of the variable matrix the small are full changes of adiabatic invariants. In case of analytic elements the full changes exponentially tend to zero when the parameter of the system tends to zero. Some part of the work has been done using Mathematica 3.0.

Date received: March 31, 1999