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The Scientific World Journal
Volume 2014, Article ID 819290, 8 pages
Research Article

Birkhoff Normal Forms and KAM Theory for Gumowski-Mira Equation

1Department of Mathematics, University of Rhode Island, Kingston, RI 02881-0816, USA
2Department of Mathematics, University of Tuzla, 75000 Tuzla, Bosnia and Herzegovina
3Department of Mathematics, University of Sarajevo, 71000 Sarajevo, Bosnia and Herzegovina

Received 29 August 2013; Accepted 19 October 2013; Published 16 January 2014

Academic Editors: Z. Guo, Z. Huang, X. Song, and Y. Xia

Copyright © 2014 M. R. S. Kulenović et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


By using the KAM theory we investigate the stability of equilibrium solutions of the Gumowski-Mira equation: , where , and we obtain the Birkhoff normal forms for this equation for different equilibrium solutions.