3 papers
math.DS2026
An index theory for transverse trajectories
Nelson Schuback
In this work, we present an alternative definition of the Le Roux index, which generalizes the Poincaré-Hopf index for non-singular planar flows to the broader setting of Brouwer…
math.DS2025
A foliated viewpoint on homotopy Brouwer theory
Nelson Schuback
Brouwer homeomorphisms are fixed-point-free, orientation-preserving homeomorphisms of the plane. In recent years, their dynamics have been mostly studied through two complementary…
math.DS2025
Refined methods in foliated Brouwer theory
Nelson Schuback
A Brouwer homeomorphism is a fixed-point free, orientation-preserving homeomorphism of the plane. A foundational result of Le Calvez establishes that every such homeomorphism a…