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- W156729229 abstract "Many arithmetic geometric results have an arithmetic dynamic analogue. For instance, Siegel's theorem, that an elliptic curve has only nitely many integer points, is analogous to the fact that any orbit under a rational function whose second iterate has a non-constant denominator has only nitely many distinct integer values. A conjecture of Lang states that the number of integer points on a minimal Weierstrass model of an elliptic curve is uniformly bounded. In order to translate this conjecture, one needs a dynamic concept of minimality. We present two such notions, a ne minimality and full PGL2(Q)-minimality, and prove they are equivalent. We also present an algorithm to test minimality. Finally, we present the results of an exhaustive search for rational functions with many integers in an orbit. These provide the best known minima for uniform bounds on the number of integers in orbits." @default.
- W156729229 created "2016-06-24" @default.
- W156729229 creator A5062310226 @default.
- W156729229 date "2011-09-09" @default.
- W156729229 modified "2023-09-27" @default.
- W156729229 title "Fractional linear minimal models of rational functions" @default.
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