Dynamics of Rational Surface Automorphisms: Linear Fractional Recurrences

dc.creatorBedford, Eric
dc.creatorKim, Kyounghee
dc.date2006-11-09
dc.date2009-03-10
dc.date.accessioned2026-07-07T12:50:39Z
dc.date.available2026-07-07T12:50:39Z
dc.descriptionWe consider the family $f_{a,b}(x,y)=(y,(y+a)/(x+b))$ of birational maps of the plane and the parameter values $(a,b)$ for which $f_{a,b}$ gives an automorphism of a rational surface. In particular, we find values for which $f_{a,b}$ is an automorphism of positive entropy but no invariant curve. The Main Theorem: If $f_{a,b}$ is an automorphism with an invariant curve and positive entropy, then either (1) $(a,b)$ is real, and the restriction of $f$ to the real points has maximal entropy, or (2) $f_{a,b}$ has a rotation (Siegel) domain.
dc.description24 pages, 7 figures, A companion Mathematica notebook is available at: http://www.math.fsu.edu/~kim/
dc.identifierhttps://arxiv.org/abs/math/0611297
dc.identifierhttp://arxiv.org/abs/math/0611297
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/222747
dc.subjectDynamical Systems
dc.subject37F99;32M99;32H50
dc.titleDynamics of Rational Surface Automorphisms: Linear Fractional Recurrences
dc.typetext

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