Session S14 - Global Injectivity, Jacobian Conjecture, and Related Topics

Monday, July 12, 12:50 ~ 13:40 UTC-3

Geometric ideas on injectivity applied to discrete dynamics

Eduardo C. Balreira

Trinity University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

A central question in discrete dynamics is to establish when a map has a globally asymptotically stable fixed point. This can be naturally framed as a question of injectivity. We will discuss how geometric methods to detect injectivity can be applied in this area. We will illustrate how new results on monotone maps in terms of preservation of normals to hypersurfaces generalizes the classical work for monotone maps in the plane. In addition, these ideas provide new insight on a geometric generalization of the Gale-Nikaido conjecture, at least for the planar case.

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