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Progress in normal form theory. (English) Zbl 1175.37002
The paper is a survey of recent results about normal forms of systems of analytic differential equations near a fixed point. It includes (among others) examples of Hamiltonian, volume preserving, quasihomogeneous vector fields. It discusses diophantine conditions relevant to the convergence of solutions.

MSC:
37-02 Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory
34-02 Research exposition (monographs, survey articles) pertaining to ordinary differential equations
37C10 Dynamics induced by flows and semiflows
34M25 Formal solutions and transform techniques for ordinary differential equations in the complex domain
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