English

On a dynamical version of a theorem of Rosenlicht

Algebraic Geometry 2014-08-21 v1 Dynamical Systems Number Theory

Abstract

Consider the action of an algebraic group GG on an irreducible algebraic variety XX all defined over a field kk. M. Rosenlicht showed that orbits in general position in XX can be separated by rational invariants. We prove a dynamical analogue of this theorem, where GG is replaced by a semigroup of dominant rational self-maps of XX. Our semigroup GG is not required to have the structure of an algebraic variety and can be of arbitrary cardinality.

Keywords

Cite

@article{arxiv.1408.4744,
  title  = {On a dynamical version of a theorem of Rosenlicht},
  author = {Jason P. Bell and Dragos Ghioca and Zinovy Reichstein},
  journal= {arXiv preprint arXiv:1408.4744},
  year   = {2014}
}