Discrete Orbits,Recurrence and Solvable Subgroups of $${{\mathrm{Diff}}\, ({{\mathbb {C}}}^2, 0)}$$ |
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Authors: | Julio C Rebelo Helena Reis |
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Institution: | 1.Institut de Mathématiques de Toulouse,Toulouse,France;2.Centro de Matemática da Universidade do Porto,Faculdade de Economia da Universidade do Porto,Porto,Portugal |
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Abstract: | 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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