284 reputation
1530
bio website profs.du.ac.ir/info/taghavi
location Iran
age 43
visits member for 1 year, 5 months
seen 15 hours ago

I am interested in finding some new interpretations for:

"The number of limit cycles of a polynomial vector field"

In particular, I am interested in the following $8$ questions:

elliptic operators corresponds to non vanishing vector fields

Codimension of the range of certain linear operators

Limit cycles as closed geodesics(geodesible flow)

The error in Petrovski and Landis' proof of the 16th Hilbert problem

Lifting a quadratic system to a non vanishing vector field on $S^{3}$ or $T^{1} S^{2}$

The integral of torsion

The Moyal action of a planar vector field

A question on "The weakened Hilbert 16th problem"

When I was a PHD student, working on limit cycle theory, my supervisor encouraged me to learn the elements and basics of Noncommutative Geometry, in order to find a possible new interpretation for the number of limit cycles of a vector field. He also suggested me to think about a possible relation between $H(2)$ and Hyperbolic geometry. He also encouraged me to learn the elements of Conley index theory to find a possible relation to limit cycle theory.


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