Abstract

Hamilton Systems with a Small Parameter:Approximate Symmetries and First Integrals

V.Baikov (Ufa State Aviation Technical University, Ufa, Russia)

e-mail: baikov@math.ugatu.ac.ru.

We consider hamilton systems with a small parameter which Hamilton function may be written in the form H=H_0(I)+\\varepsilon H_1(I, \varphi,t), where I, \varphi are vectors of angle-action variables, t is a time, \varepsilon is a small parameter of pertubation and H_0(I) is corresponding to non-pertubed motion. Theorem of inheritance of all exact symmetries is proved. Also we investigate so called hamilton symmetries which are related with first integrals. For these symmetries it may be shown that during inheritance procedure they are still hamilton. Moreover, in this sense approximate first integrals could be found. Such symmetries are used for constructing of approximate solutions.

Section : 12