Dynamics of Rational Surface Automorphisms: Linear Fractional Recurrences
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...
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| Veröffentlicht in: | The Journal of geometric analysis 2009-07, Vol.19 (3), p.553-583 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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. |
|---|---|
| ISSN: | 1050-6926 1559-002X |
| DOI: | 10.1007/s12220-009-9077-8 |