About Dulac's Problem in R3 for Perturbations of Linear Non-Degenerated Centers

About Dulac's Problem in R3 for Perturbations of Linear Non-Degenerated Centers

Explore a 40-minute lecture on Dulac's problem in $\mathbb{R}^3$ for perturbations of linear non-degenerated centers, presented by María Martín Vega from the University of Valladolid at the Fields Institute. Delve into the intricacies of geometric and model theory, covering topics such as Poincaré First Return map, local sets of cycles, blowing up of singularities, and the analysis of two-dimensional systems. Examine the application of flow boxes, invariant surfaces, and the Poincaré map to understand the accumulation of cycles in the axis direction. Gain insights into the analytical approach to Dulac's problem and its implications for semihyperbolic cases.