Periodicity and boundedness for the integer solutions to a minimum-delay difference equation

Abstract

In this paper, we study periodicity and boundedness for the integer solutions to a minimum-delay difference equations. As an application, a recent theorem regarding absolute-difference equations is extended.

Keywords:

• minimum-delay difference equations
• piecewise difference equations
• periodicity
• recursive equation
• composition-delay equations
• growth rates

2000 Mathematics Subject Classification::

• 39A10
• 39A11

Acknowledgements

We are very thankful to a referee for comments and insights that substantially improved this manuscript. In addition, we are grateful to Miaohua Jiang and C. Adam Cross for useful discussions. The first author acknowledges support from an Archie Fund grant.

Notes

1. [email protected]

2. Apparent unboundedness of particular solutions was verified by approximate computation.

Additional information

Notes on contributors

Richard T. Guy

1