Book Review: Normal forms and bifurcations of planar vector fields

Unique Normal Forms for Nilpotent Planar Vector Fields

Hilbert's 16th Problem and bifurcations of Planar Polynomial Vector Fields

The original Hilbert’s 16th problem can be split into four parts consisting of Problems A–D. In this paper, the progress of study on Hilbert’s 16th problem is presented, and the relationship between Hilbert’s 16th problem and bifurcations of planar vector fields is discussed. The material is presented in eight sections. Section 1: Introduction: what is Hilbert’s 16th problem? Section 2: The fir...

Normal Forms and Bifurcation of Planar Vector Fields (Shee-Nee Chow, Chengzhi Li, and Duo Wang)

Bifurcations of Optimal Vector Fields

We study the structure of the solution set of a class of infinite-horizon dynamic programming problems with one-dimensional state spaces, as well as their bifurcations as problem parameters are varied. The solutions are represented as the integral curves of a multi-valued ‘optimal’ vector field on state space. Generically, there are three types of integral curves: stable points, open intervals ...

Normal Forms of Vector Fields on Poisson Manifolds

We study formal and analytic normal forms of radial and Hamiltonian vector fields on Poisson manifolds near a singular point.