A Class of Globally Hypoelliptic Operators on the Torus.
Summability of first integrals of a -non-integrable resonant Hamiltonian system
This article studies the summability of first integrals of a -non-integrable resonant Hamiltonian system. The first integrals are expressed in terms of formal exponential transseries and their Borel sums. Smooth Liouville integrability and a relation to the Birkhoff transformation are discussed from the point of view of the summability.
Simultaneous reduction to normal forms of commuting singular vector fields with linear parts having Jordan blocks
We study the simultaneous linearizability of –actions (and the corresponding -dimensional Lie algebras) defined by commuting singular vector fields in fixing the origin with nontrivial Jordan blocks in the linear parts. We prove the analytic convergence of the formal linearizing transformations under a certain invariant geometric condition for the spectrum of vector fields generating a Lie algebra. If the condition fails and if we consider the situation where small denominators occur, then...
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