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PEM

Seminar

Diophantine integrability

Halburd, R (Loughborough)
Monday 18 September 2006, 15:30-16:30

Seminar Room 1, Newton Institute

Abstract

Discrete equations over the rational numbers (and more generally over number fields) will be considered. The height of a rational number a/b is max(a,b), where a and b are coprime. The height of the nth iterate of an equation appears to grow like a power of n for discrete equations broadly considered to be of Painlev\'e type, and exponentially for other equations. Methods for classifying equations according to this criterion will be described. Connections with other approaches, such as Nevanlinna theory, singularity confinement and algebraic entropy, will be discussed.

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