On the Number and Position of Poincaré Limit Cycles

[Guest]

"What is the number and position of Poincaré Limit Cycles (isolated periodic solutions) for a polynomial differential equation:

[tex]\frac{dy}{dx} = \frac{P(x, y)}{Q(x,y)}[/tex],

where P and Q are polynomials of degree n?"

Relevant Reference Links:

'Around Hilbert Sixteenth Problem',

http://www.wisdom.weizmann.ac.il/~yakov/ftpapers/Book/intro.pdf;

'David Hilbert's Sixteenth Problem',

https://en.wikipedia.org/wiki/Hilbert%27s_sixteenth_problem.

[Guest]

FYI: 'Theory of Limit Cycles' by Prof. YE YAN-QIAN et al.,

https://epdf.pub/theory-of-limit-cycles-translations-of-mathematical-monographs.html.

[Guest]

FYI: 'On the limit cycle of the Liénard equation' by Prof. K. Odani,

https://dml.cz/bitstream/handle/10338.dmlcz/107715/ArchMathRetro_036-2000-1_4.pdf.

Enjoy!

[Guest]

FYI: 'A Constructive Solution to the Infinitesimal Hilbert 16th Problem (Year 2008)',

http://www.wisdom.weizmann.ac.il/~www/pages/milestones/2008_1.html.