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Chapter
![On the Number of Limit Cycles for the Equation
d
y
d
x
=
P
(
x
,
y
)
Q
(
x
,
y
)
, where P and Q are Polynomials of Degree 2
*
[
1
]](https://images.tandf.co.uk/common/jackets/crclarge/978036781/9780367810504.jpg "On the Number of Limit Cycles for the Equation
d
y
d
x
=
P
(
x
,
y
)
Q
(
x
,
y
)
, where P and Q are Polynomials of Degree 2
*
[
1
]")
Chapter
On the Number of Limit Cycles for the Equation d y d x = P ( x , y ) Q ( x , y ) , where P and Q are Polynomials of Degree 2 * [ 1 ]
DOI link for On the Number of Limit Cycles for the Equation d y d x = P ( x , y ) Q ( x , y ) , where P and Q are Polynomials of Degree 2 * [ 1 ]
On the Number of Limit Cycles for the Equation d y d x = P ( x , y ) Q ( x , y ) , where P and Q are Polynomials of Degree 2 * [ 1 ]
ABSTRACT
A closed one-dimensional curve on graph we call a cycle. A cycle is said to be homologous to zero if it coincides with the border of a part of the integral curve, where K is a compact set. Two cycles on the integral curve are said to be homologous to one another if their union forms the border of a compact part of the integral curve. A cycle of the real equation that is stable with respect to a* cannot be homotopic to zero on an integral curve of the corresponding complex equation. For the real equation, the maximal number of limit cycles that are stable with respect to a does not exceed the maximal number of cycles for the complex equation that are simple, correctly located and non-homotopic to zero and each other.
