46 citations · 57 across the 11 of their papers we have counts for
5 papers · 2 filters
A note on focus-focus singularities
Nguyen Tien Zung
We give a topological and geometrical description of focus-focus singularities of integrable Hamiltonian systems. In particular, we explain why the monodromy around these singulari…
Another note on focus-focus singularities
Nguyen Tien Zung
We show a natural relation between the monodromy formula for focus-focus singularities of integrable Hamiltonian systems and a formula of Duistermaat-Heckman, and extend the main r…
Symplectic topology of integrable Hamiltonian systems, I: Arnold-Liouville with singularities
Nguyen Tien Zung
The classical Arnold-Liouville theorem describes the geometry of an integrable Hamiltonian system near a regular level set of the moment map. Our results describe it near a nondege…
Convergence versus integrability in Poincare-Dulac normal form
Nguyen Tien Zung
We show that, to find a Poincare-Dulac normalization for a vector field is the same as to find and linearize a torus action which preserves the vector field. Using this toric chara…
Convergence versus integrability in Birkhoff normal form
Nguyen Tien Zung
We show that any analytically integrable Hamiltonian system near an equilibrium point admits a convergent Birkhoff normalization. The proof is based on a new, geometric approach to…