Duke Mathematical Journal

Periodic points of birational transformations on projective surfaces

Xie Junyi

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Abstract

We give a classification of birational transformations on smooth projective surfaces which have a Zariski-dense set of noncritical periodic points. In particular, we show that if the first dynamical degree is greater than one, the union of all noncritical periodic orbits is Zariski-dense.

Article information

Source
Duke Math. J., Volume 164, Number 5 (2015), 903-932.

Dates
First available in Project Euclid: 7 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1428419275

Digital Object Identifier
doi:10.1215/00127094-2877402

Mathematical Reviews number (MathSciNet)
MR3332894

Zentralblatt MATH identifier
06436784

Subjects
Primary: 37P55: Arithmetic dynamics on general algebraic varieties 37C25: Fixed points, periodic points, fixed-point index theory
Secondary: 14J50: Automorphisms of surfaces and higher-dimensional varieties

Keywords
birational transformation projective surface dynamical degree periodic point Zariski dense

Citation

Junyi, Xie. Periodic points of birational transformations on projective surfaces. Duke Math. J. 164 (2015), no. 5, 903--932. doi:10.1215/00127094-2877402. https://projecteuclid.org/euclid.dmj/1428419275


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