Hilbert's 16th problem. When variational principles meet differential systems

TL;DR

This paper discusses the challenges and ongoing efforts to accurately count limit cycles in differential systems related to Hilbert's 16th problem, highlighting the importance of variational principles.

Contribution

It introduces a revised approach to counting limit cycles, addressing previous errors and advancing understanding in the field.

Findings

Identified a mistake in previous limit cycle counting methods

Developed a new approach using variational principles

Ongoing work to refine the counting technique

Abstract

Thanks to the interest of many people, a mistake has been found in our way of counting limit cycles. We are working on a new version.