Focal values of plane cubic centers
Hans-Christian Graf v. Bothmer, Jakob Kr\"oker
TL;DR
This paper demonstrates that having the first 11 focal values vanish is not enough to guarantee a plane cubic system has a center, challenging previous assumptions.
Contribution
It provides a counterexample showing the insufficiency of 11 focal values for center conditions in plane cubic systems.
Findings
Vanishing of 11 focal values does not imply a center
Counterexample disproves previous conjectures
Highlights need for additional conditions
Abstract
We prove that the vanishing of 11 focal values is not sufficient to ensure that a plane cubic system has a center.
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