Bounded solutions of a class of difference equations in Banach spaces producing controlled chaos

Stevo Stević

Chaos, Solitons & Fractals, 2008, vol. 35, issue 2, 238-245

Abstract: Let X be a complex Banach space, αj, j=1,…,k, be real numbers, with ∑j=1kαj=1 and let (xn)n∈N be a sequence in X such thatlimn→∞xn+k-∑j=1kαjxn+k-j=0.It is given a sufficient and necessary condition such that the boundedness of (xn)n∈N always implies limn→∞∥xn+1−xn∥=0. We also present a sufficient condition which guarantees that every slowly varying solution of the difference equation xn+1=f(xn,…,xn−k) is convergent, if f is a real function.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:35:y:2008:i:2:p:238-245

DOI: 10.1016/j.chaos.2007.07.037

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