Dynamics of Rational Surface Automorphisms: Linear Fractional Recurrences
| dc.creator | Bedford, Eric | |
| dc.creator | Kim, Kyounghee | |
| dc.date | 2006-11-09 | |
| dc.date | 2009-03-10 | |
| dc.date.accessioned | 2026-07-07T12:50:39Z | |
| dc.date.available | 2026-07-07T12:50:39Z | |
| dc.description | We 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.description | 24 pages, 7 figures, A companion Mathematica notebook is available at: http://www.math.fsu.edu/~kim/ | |
| dc.identifier | https://arxiv.org/abs/math/0611297 | |
| dc.identifier | http://arxiv.org/abs/math/0611297 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222747 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37F99;32M99;32H50 | |
| dc.title | Dynamics of Rational Surface Automorphisms: Linear Fractional Recurrences | |
| dc.type | text |