Fixed points and periodic points for maps that are expansive in one direction, with applications., Fabio Zanolin (Università degli Studi di Udine, Italy)
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Monday, 28. March 2022, 15:00
- Abstract: In the first part of the talk, I will describe a geometric approach, based on the theory of topological horseshoes, to prove the existence of fixed points, periodic points, and complex dynamics for maps that are defined in rectangular regions of the plane and which are expansive in one direction. In the second part of the talk, I will present some applications to periodically perturbed planar systems in which the unperturbed system has a center (local or global) with an associated monotone period map. In this case, the results can be seen as a natural variant of the classical Poincaré-Birkhoff fixed point theorem, in which the usual twist condition on the angular coordinate is paired with a compression/expansion condition on the radial component.