Induced Vector Fields Research Articles

The global dynamics of a class of nonlinear vector fields in R3

In this paper, we study the geometric properties of a class of nonlinear poly- nomial vector fields in R 3 . By virtue of their induced vector fields, their global topo- logical structures are discussed and we get that there are at least 82 types of invariant regions with different topological classification without considering the closed orbit. Finally, we give a sufficient condition of the existence of a closed orbit of the vector field.

The associated map of the nonabelian Gauss-Manin connection

The Gauss-Manin connection for nonabelian cohomology spaces is the isomonodromy flow. We write down explicitly the vector fields of the isomonodromy flow and calculate its induced vector fields on the associated graded space of the nonabelian Hogde filtration. The result turns out to be intimately related to the quadratic part of the Hitchin map.

A projective Dirac operator on $ \mathbb{C}{P^2} $ within fuzzy geometry

We propose an ansatz for the commutative canonical spin_c Dirac operator on CP^2 in a global geometric approach using the right invariant (left action-) induced vector fields from SU(3). This ansatz is suitable for noncommutative generalisation within the framework of fuzzy geometry. Along the way we identify the physical spinors and construct the canonical spin_c bundle in this formulation. The chirality operator is also given in two equivalent forms. Finally, using representation theory we obtain the eigenspinors and calculate the full spectrum. We use an argument from the fuzzy complex projective space CP^2_F based on the fuzzy analogue of the unprojected spin_c bundle to show that our commutative projected spin_c bundle has the correct SU(3)-representation content.

Avoiding ergodicity and turbulence in [formula omitted] vector fields

We show that analytic R 3 vector fields having the property of being transversal to either analytic functions or foliations F 2 , or parallel to a foliation, are free from ergodicity and turbulence. The absence of turbulence and ergodicity via induced vector fields is also proven.

Linearly induced vector fields and $\mathbf{R}^2$-actions on spheres

Linearly induced vector fields and $\mathbf{R}^2$-actions on spheres