Recurrent orbits of subgroups of local complex analytic diffeomorphisms. (English) Zbl 1360.32013
Summary: We show recurrent phenomena for orbits of groups of local complex analytic diffeomorphisms that have a certain subgroup or image by a morphism of groups that is non-virtually solvable. In particular we prove that a non-virtually solvable subgroup of local biholomorphisms has always recurrent orbits, i.e. there exists an orbit contained in its set of limit points.
MSC:
| 32H50 | Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables |
| 37C85 | Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\) |
| 20F16 | Solvable groups, supersolvable groups |
| 37F75 | Dynamical aspects of holomorphic foliations and vector fields |
| 20F14 | Derived series, central series, and generalizations for groups |
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