Osipenko GS and Korzh TN
The aim is substantiation of a constructive method for verification of structural stability of discrete dynamical systems. The hyperbolicity of the chain recurrent set is a necessary condition for the structural stability. If the spectrum of the differential Df does not contain 0, then the chain recurrent set is hyperbolic and the system is Ω-stable. The spectrum is estimated through the symbolic image of operation of the differential on projective bundle. A diffeomorphism f is shown to be structurally stable if and only if the spectrum of complementary differential Df ˆ does not contain 0 and there is no connection CR+→CR on the projective bundle, where CR+ and CR denote the chain recurrent components for the positive and negative parts of the spectrum. These conditions are verified through the symbolic image of the complementary differential.
English 
Spanish 
Chinese 
Russian 
German 
French 
Japanese 
Hindi