George Osipenko
St. Petersburg State Technical University, Russia
Serpil Pehlivan
Suleyman Demirel Univrsity, Turkey
By summing results by J. Robin, C. Robinson and R. Mane one can formulate the theorem that in order to a diffeomorphism f: M→ M be structurally stable it is necessary and sufficient that the transversality condition holds on the manifold M. Thus Theorem solves the problem of structural stability. However application of this result is limited by difficulties of verification of the transversality condition. This paper describes the equivalent necessary and sufficient conditions for the structural stability and moreover a finite algorithm for the verification is given. The described algorithm is based on the applied symbolic dynamics methods.