A note on the geometry of invariants

We present a short geometric proof that the difference equation

admits an invariant which is continuous and which separates solutions as efficiently as possible. The existence of invariants for a wide class of equations, including this one, has been recently established (see, R. Abus-Saris and Q. Al-Hassan, 2005 On globally attracting two-cycles of second order difference equations, Journal of Difference Equations and Applications 11, 1295–1303). This note presents an alternative and conceptually simpler approach.

Keywords:

• Difference equation
• Planar mapping
• Invariant

Notes

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Additional information

Notes on contributors

Aaron S. Clark

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D. R. Wilken

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