Birkhoff Normal Forms and KAM Theory for Gumowski-Mira Equation. (16th January 2014)

• Record Type: Journal Article
• Authors: Kulenović, M. R. S.; Nurkanović, Z.; Pilav, E.
• Other Names: Guo Z. Academic Editor.; Huang Z. Academic Editor.; Song X. Academic Editor.; Xia Y. Academic Editor.
• Is Part Of: TheScientificWorldjournal. Volume 2014(2014)
• Publication Date: 2014-01-16
• Subjects: Science -- Periodicals; Technology -- Periodicals; Medicine -- Periodicals; 505
• DOI: 10.1155/2014/819290
• Languages: English
• ISSNs: 2356-6140

Abstract

Abstract : By using the KAM theory we investigate the stability of equilibrium solutions of the Gumowski-Mira equation: x n + 1 = ( 2 a x n ) / ( 1 + x n 2 ) - x n - 1, n = 0, 1, …, where x - 1, x 0 ∈ ( - ∞, ∞ ), and we obtain the Birkhoff normal forms for this equation for different equilibrium solutions.