Work

Global linearization of asymptotically stable systems without hyperbolicity

Year: 2025

Type: article

Abstract: We give a proof of an extension of the Hartman-Grobman theorem to nonhyperbolic but asymptotically stable equilibria of vector fields. Moreover, the linearizing topological conjugacy is (i) defined on the entire basin of attraction if the vector field is complete, and (ii) a -diffeomorphism on the complement of the equilibrium if the vector field is and the underlying space is not 5-dimensional. We also show that the statement in the 5-dimensional case is equivalent to the 4-dimensional smooth Poincaré conjecture.

Source: Systems & Control Letters

DOI: 10.1016/j.sysconle.2025.106163

Authors: Matthew D. Kvalheim, Eduardo D. Sontag

Institutions: University of Maryland, Baltimore County, Northeastern University

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,910

Funder: Air Force Office of Scientific Research