Title

Invariants and related Liapunov functions for difference equations

Document Type

Article

Date of Original Version

9-1-2000

Abstract

Consider the difference equation xn+1 = f(xn), where xn is in Rk and f : D → D is continuous where D ⊂ Rk. Suppose that I : Rk → R is a continuous invariant, that is, I(f(x)) = I(x) for every x ∈ D. We will show that if I attains an isolated minimum or maximum value at the equilibrium (fixed) point p of this system, then there exists a Liapunov function, namely ±(I(x) - I(p)) and so the equilibrium p is stable. This result is then applied to some difference equations appearing in different fields of applications. © 2000 Elsevier Science Ltd. All rights reserved.

Publication Title

Applied Mathematics Letters

Volume

13

Issue

7

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