On Coxeter recurrences

Abstract

An interesting family of recurrences of order n ≥ 2, which are globally (n+3)-periodic was introduced by Coxeter in 1971. We prove a surprising property of this family: ‘all’ the possible geometrical behaviours that linear real (n+3)-periodic recurrences can have are present inside the Coxeter recurrences.

2000 Mathematics Subject Classification::

• 39A05
• 39A20
• 39B12

Keywords:

• globally periodic difference equations
• recurrences
• Coxeter difference equations
• linearization

Acknowledgements

The first and second authors are partially supported by a MCYT/FEDER grant no. MTM2008-03437. The third author by a MCYT/FEDER grant no. MTM2008-01486. All are also supported by a CIRIT grant no. 2009SGR 410.

Notes

1. [email protected]

2. [email protected]

Additional information

Notes on contributors

Armengol Gasull

1

Francesc Mañosas

2