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1. 5. 2009.
Attractivity and global stability for linearizable difference equations
Consider the difference equation x"n"+"1=f(x"n,...,x"n"-"k),n=0,1,... where [email protected]?{0,1,...} and the initial conditions are real numbers. We use the linearization of this equation in the form x"n"+"[email protected]?i=1-lkg"ix"n"-"i,n=0,1,... where [email protected]?{1,2,...} and the functions g"i:R^k^+^l->R to investigate the asymptotic behavior of the solutions of the considered equation. We illustrate our results with various examples.