 

Solomon Vishkautsan
Arithmetic dynamics on smooth cubic surfaces view print


Published: 
January 15, 2014

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


Abstract
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 localglobal property called strong residual periodicity. Finally, we give a dynamical result relating to the MordellWeil problem on cubic surfaces.


Acknowledgements
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 BenGurion University of the Negev.


Author information
Department of Mathematics, BenGurion University of the Negev, P.O.B. 653 BeerSheva 8410501 Israel
wishcow@gmail.com

