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International Conference on Mathematical Modeling and Scientific Computing
April 2-6, 2001
Middle East Technical University and Selcuk University
Ankara and Konya, Turkey

Organizers
F. Bornemann (Munich University of Tecnology, Germany), H. Bulgak (Selcuk University, Konya, Turkey), V. Ganzha (Munich University of Technology, Germany), B. Karasozen (METU, Ankara, Turkey), A. Sinan (Selcuk University, Konya, Turkey), C. Zenger (Munich University of Technology, Germany)

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Applied Symbolic Dynamics Verification of Structure Stability
by
George Osipenko
Department of Mathematics, Suleyman Demirel University and Nonlinear Analysis and Mathematical Modeling Laboratory, St, Petersburg University, Russia
Coauthors: Sepil Pehlivan (Department of Mathematics, Suleyman Demirel University, Isparta)

By summing results by J. Robin, R. 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 the heorem 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.

Date received: February 13, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagk-50.