Normal Form Method and Formal Integrals of Nonlinear ODEs systems
                        Victor F. Edneral

    Institute for Nuclear Physics of Moscow State University
             Leninskie Gory, Moscow, 119899, Russia

                e-mail: edneral@theory.npi.msu.su
                  Phone/fax: (+7+095) 939-03-97

    This  report  describes  examples of  building  by  the  NORT 
package and a practical usage of formal integrals of  Gustavson's 
type  for  the  reduction of an  order  of  nonlinear  autonomous 
systems of ODEs.  The formal integrals are created by the  normal 
form  method  as  a truncated power series in  variables  of  the 
system. For relevant cases (for example for Henon-Heiles' system) 
this technique provides exact formal integrals so it is  possible 
to  get some partial periodic solutions of nonlinear  systems  in 
these  cases.  Otherwise it is possible to get approximations  of 
formal  integrals  which  can  be  useful  for  increasing  of  a 
precision of a numerical integration of periodic solutions of the 
systems.