Abstract |

**Resolving Systems Reduction
Possibilities in Stationary Bifurcation Theory**

*I.V.Konopleva, B.V.Loginov (Department
of Higher Mathematics, Ulyanovsk State Technical University, Ulyanovsk, Russia)*

*e-mail:
loginov@ulstu.ru*

In
Banach spaces it is considered nonlinear equation with complex bifurcational
parameter and densely defined closed linear Fredholm operators, the nonlinear
term is sufficiently smooth. Beginning with the first works (V.I.Yudovich
(1967), B.V. Loginov and V.A. Trenogin (1971)) on the usage of group symmetry
conditions for nonlinear equation the question about simultaneous reduction of
branching equation (BEq) on unknowns and equations (truncation reduction) has
remained open. Here it is solved for the
more general finitedimensional equivalent of nonlinear equation - BEq in the
root subspace (BEqR). As corollary we obtain the corresponding results for Beq.
The results and designations of our communications on the Kasnoyarsk
international Conference "Symmetry and differential equations"-2000
and previous MOGRAN-VIII are used.

Section
: 12