Dynamic systems can be classified, among others, by looking at the behavior of nearby points. If the points remain close during the movement, we speak of elliptical systems. If the points move away with exponential speed (like the clouds in the Earth's atmosphere) we speak of hyperbolic systems. In the middle there is a wide class of systems called parabolics, whose study has been developed in the last fifty years. One group that has been widely studied is that of parabolic flows. These are unipontent flows in Lie groups and are of interest for geometrical and number theory problems. They are studied through algebraic and representation theory methods. There are important aspects to be investigated through the study of examples of perturbations of these unipotent flows, which, although parabolic, destroy the algebraic structure. In our work we will show that these perturbations are fundamentally different from the original flows, and therefore constitute a new class of parabolic flows.
|Effective start/end date||9/21/20 → 3/22/22|
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