The second part of the Hilbert's 16th problem (determination of the upper bound on the number of limit cycles for two-dimensional polynomial vector fields of given degree), proposed in 1900, is still open and a bit mysterious. Its varìous aspects have been frequently revisited, "proven" and disproven! In particular, Petrovskiĭ and Landis claimed that they solved this problem in 1950s, but their "proof" turned out to have a gap. There is a related discussion on Mathematics Overflow.
Here is my question: I
Does there exist a paper which explicitly describe the essential mistake in that famous paper of Petrovski and Landis? Am I correct to think that there is no universal agreement as to existence of such a paper?