Duke Mathematical Journal

Periodic points of birational transformations on projective surfaces

Xie Junyi

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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

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

First available in Project Euclid: 7 April 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

birational transformation projective surface dynamical degree periodic point Zariski dense


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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