Mirror transformations of Hamiltonian systems

Painleve Test and the Resolution of Singularities for Integrable Equations

“…The corresponding leading coefficients are 1, 0, −1, 1. The Hénon-Heiles system in [12] is another example. When the Fuchsian condition is satisfied, we denote the dominant part of…”

“…The exact meaning of the "Hamiltonian way" is given in Section 3. See [12] for some concrete examples.…”

A New Perturbative Approach in Nonlinear Singularity Analysis

“…Firstly, the success of constructing mirror transformations enables us to treat each principal balance in the Painleve test, singularity structures and symplectic structures of Hamiltonian systems from a common point of view. Secondly, Hu et al (2001) showed that the mirror transformations are canonical for finite-dimensional Hamiltonian systems. Moreover, Yee (2002) demonstrated that the linearization of mirror systems near movable poles gives the possibility to construct the associated Backlund transformations of some partial differential equations and the Schlesinger transformations of some ordinary differential equations.…”