In this paper we prove that braid monodromy of an affine plane curve determines the topology of a related projective plane curve. Introduction Our purpose in this paper is to relate the topological embedding of algebraic curves to a refinement of a well-known invariant of curves such as braid monodromy. Roughly speaking, braid monodromy is defined for a triple (C , L , P), where C ⊂ P2 is a cur...

Given a nilpotent singular point of planar vector field, its monodromy is associated with Andreev number n. The parity n determines whether the existence an inverse integrating factor implies that center. For odd, this not always true. We give characterization for family systems having such center problem cannot be solved by method. Moreover, we study general properties family, determining nece...

SOLVMANIFOLD DARYL COOPER AND MARTIN SCHARLEMANN Abstract. We classify isotopy classes of Heegaard splittings of solvmanifolds. If the monodromy of the solvmanifold can be expressed as m 1 1 0 ; for some m 3 (as always is true when the trace of the monodromy is 3), then any irreducible splitting is strongly irreducible and of genus two. If m 4 any two such splittings are isotopic. If m = 3 then...

In this paper we study a special class of monodromy evolving deformations (MED), which represents Halphen’s quadratic system. In 1996, Chakravarty and Ablowitz [4] showed that a fifth-order equation (DH-V) ω 1 = ω2ω3 − ω1(ω2 + ω3) + φ , ω 2 = ω3ω1 − ω2(ω3 + ω1) + θ , ω 2 = ω3ω1 − ω2(ω3 + ω1)− φθ, (1) φ = ω1(θ − φ) − ω3(θ + φ), θ = −ω2(θ − φ)− ω3(θ + φ), which arises in complex Bianchi IX cosmol...

We revisit the roller-coaster cosmology based on multiple stages of monodromy inflation. Working within framework effective flux field theory, we include full range strong coupling corrections to inflaton sector. find that flattened potentials $V\ensuremath{\sim}{\ensuremath{\phi}}^{p}+\ensuremath{\cdots}$ with $p\ensuremath{\lesssim}1/2$, limited $N\ensuremath{\lesssim}25\ensuremath{-}40$ $e$-...