Normal forms for certain singularities of vectorfields

Normal forms of Hopf Singularities: Focus Values Along with some Applications in Physics

This paper aims to introduce the original ideas of normal form theory and bifurcation analysis and control of small amplitude limit cycles in a non-technical terms so that it would be comprehensible to wide ranges of Persian speaking engineers and physicists. The history of normal form goes back to more than one hundreds ago, that is to the original ideas coming from Henry Poincare. This tool p...

Enumeration and Normal Forms for Singularities in Cauchy-Riemann Structures

Starting on the next page is the 16-page Chapter II excerpted from my dissertation, “Enumeration and Normal Forms for Singularities in CauchyRiemann Structures,” 1997, University of Chicago. I have made a few minor editorial modifications so that Chapter II can be read without referring to the other Chapters. Section 5 of Chapter II is a summary of results appearing in my unpublished lecture no...

Normal Forms for Symplectic Maps with Twist Singularities

We derive a normal form for a near-integrable, four-dimensional symplectic map with a fold or cusp singularity in its frequency mapping. The normal form is obtained for when the frequency is near a resonance and the mapping is approximately given by the time-T mapping of a two-degree-of freedom Hamiltonian flow. Consequently there is an energy-like invariant. The fold Hamiltonian is similar to ...

Orbital Normal Forms for a family of-zero Singularity

Consider a Dynamical system x'=F(x,µ) such that its linear part has a pair of imaginary eigenvalues and one zero eigenvalue (Hopf zero singularity). Recently, the simplest normal form for this singular system has been obtained by sl(2) Lie algebra theory and the decomposition of space into three invariant subspaces. The normal form of this singular system is divided into three general cases. In...

Physical Interpretation of Certain Strong Coupling Singularities