split - Polynomial in Vector Field

surem

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Hi, This is a math help forum. If you need help then please tell us specifically where you are having trouble. Understand that this is not a submit your problem to us and we will solve it for you forum. In the end you will solve the problem!

Suppose Y=(P,D) be a polynomial vector field of degree 2 in R2

Please, how can I apply the fact Y has at most four isolated singularities
 
Suppose Y=(P,D) be a polynomial vector field of degree 2 in R2

Please, how can I apply the fact Y has at most four isolated singularities

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "
Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting
 
Hi!

What are your thoughts?Please share your work with us ...even if you know it is wrong If you are stuck at the beginning tell us and we'll start with the definitions. You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:http://www.freemathhelp.com/forum/th...Before-Posting

Please, I have read the rules of this forum. I really find it difficult to start the proof of the question I posted and will be glad if someone can assist me to begin. Moreover, if someone have materials for such proof I welcome it.
 
Suppose Y=(P,D) be a polynomial vector field of degree 2 in R2

Please, how can I apply the fact Y has at most four isolated singularities

A singularity in polynomial - what is the mathematical definition of it?

How does the degree of polynomial affect it?
 
Hi!

The mathematical definition of four isolated singularities: P=P(x,r)= a+bx+cr+dx2+exr+fr2 ; Z=Z(x,r)=A+Bx+Cr+Dr2+Exr+Fr2
P(x,r) is having linear and quadratic part. Z(x,r) is also having linear and quadratic. I will be glad to know if that is what you mean?
 
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