Topological methods in analysis of periodic and chaotic canard-type trajectories

We investigate the role of topological methods in the analysis of canard-type periodic and chaotic trajectories. In the first part of the paper, we apply topological degree to the analysis of multi-dimensional canards. The second part is devoted to an application of a special corollary of the Poincare-Bendixson theorem to the existence of periodic two-dimensional canards.