Discrete Orbits, Recurrence and Solvable Subgroups of $${{\mathrm{Diff}}\, ({{\mathbb {C}}}^2, 0)}$$
Tóm tắt
We discuss the local dynamics of a subgroup of
$${{\mathrm{Diff}}\, ({{\mathbb {C}}}^2, 0)}$$
possessing locally discrete orbits as well as the structure of the recurrent set for more general groups. It is proved, in particular, that a subgroup of
$${{\mathrm{Diff}}\, ({{\mathbb {C}}}^2, 0)}$$
possessing locally discrete orbits must be virtually solvable. These results are of considerable interest in problems concerning integrable systems.
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