Another note on focus-focus singularities

A note on focus-focus singularities

We give a topological and geometrical description of focus-focus singularities of integrable Hamiltonian systems. In particular, we explain why the monodromy around these singularities is non-trivial, a result obtained before by J.J. Duistermaat and others for some concrete systems.

关于几乎所有奇点阶数下 $N$ 中心问题的有理非可积性的一条注记

A note on the rational non-integrability of the $N$-center problem for almost all degrees of the singularities

本文证明 $N$ 中心问题在有理弱力和中力下，除有限多个奇点阶数 $α\in(0,2)\cap\mathbb{Q}$ 外均非有理可积，并识别剩余情形及其可积必要条件。

Riemann Surface Laminations with Singularities

In these introductory notes we give the basics of the theory of holomorphic foliations and laminations. The emphasis is on the theory of harmonic currents and unique ergodicity for laminations transversally Lipschitz in CP^2 and for generic holomorphic foliations in CP^2.

Parabolicity of degenerate singularities of axisymmetric Zhukovsky case

The degenerate singularities of systems from one well-known multiparameter family of integrable systems of rigid body dynamics are studied. Axisymmetric Zhukovsky systems are considered, i.e. axisymmetric Euler tops after adding a constant gyrostatic moment. For all values of the set of parameters, excluding some hypersurfaces, it is proved that the degenerate local and semi-local singularities of the system are of the parabolic and cuspidal type, respectively. Thus these singularities are structurally stable under small perturbations of the system in the class of integrable systems. Note that…