New York Journal of Mathematics
Volume 20 (2014) 1-25


Solomon Vishkautsan

Arithmetic dynamics on smooth cubic surfaces

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Published: January 15, 2014
Keywords: Dynamical systems, cubic surfaces, periodic points, residual periodicity, arithmetic dynamics
Subject: Primary: 37P55; Secondary: 37P35, 37P05, 14G25, 14J26, 11G05

We study dynamical systems induced by birational automorphisms on smooth cubic surfaces defined over a number field K. In particular we are interested in the product of noncommuting birational Geiser involutions of the cubic surface. We present results describing the sets of K and \bar{K}-periodic points of the system, and give a necessary and sufficient condition for a dynamical local-global property called strong residual periodicity. Finally, we give a dynamical result relating to the Mordell-Weil problem on cubic surfaces.


The author's research was supported by the Israel Science Foundation, grants 657/09 and 1207/12, and by the Skirball Foundation via the Center for Advanced Studies in Mathematics at Ben-Gurion University of the Negev.

Author information

Department of Mathematics, Ben-Gurion University of the Negev, P.O.B. 653 Beer-Sheva 8410501 Israel