Pseudo-Automorphisms of 3-space: Periodicities and Positive Entropy in Linear Fractional Recurrences

Details Pseudo-Automorphisms of 3-space: Periodicities and Positive Entropy in Linear Fractional Recurrences Pseudo-Automorphisms of 3-space: Periodicities and Positive Entropy in Linear Fractional Recurrences

2011-01-08

arxiv.org/abs/1101.1614v2

Mathematics

Dynamical Systems

Scientific paper

We study the iterative behavior of the family of 3-step linear fractional recurrences and the family of birational maps they define. We determine all the possible periodicities within this family or, equivalently, the birational maps of finite order. This family also contains pseudo-automorphisms of infinite order. One such family consists of completely integrable maps, and another family consists of maps of positive entropy. Both of these families have invariant families of $K3$ surfaces.

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