Some Periodic and Non-Periodic Recursions

By M. Csörnyei, M. Laczkovich. 2001

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Periodicities in linear fractional recurrences: Degree growth of birational surface maps (2005, background): “f determining the parameter values α and β for which fα,β is periodic has been known for some time and is posed explicitly in [GKP] and [GL, p. 161]. Recent progress in this direction was obtained in [CL]. The connection with our work here is that if δ(α,β) > 1, then the degrees of the iterates o”
Root systems and generalized associahedra (2005, background): “g hypothesis, let us try to ﬁnd similar examples. What other pairs (s,s′) of linear 1The discovery of this recurrence and its 5-periodicity are sometimes attributed to R. C. Lyness (1942); see, e.g., [15]. It was probably already known to N. H. Abel. This recurrence is closely related to (and easily”
Periodicity of some classes of holomorphic difference equations (2006, methodology): “Motivated by the just mentioned research problem, Csörnyei and Laczkovich [2] investigated a special case of this general difference equation, and determined all periodic difference equations of the form xn 1⁄4 a0 þ a1xn21 þ .”