Question: Effect of Homeomorphism on Topological Properties Exp... | Filo

SOLVED: 20. Hartman-Grobman Theorem: Finding Homeomorphism H in neighborhood that establishes an isochronous flow equivalence between the flow of the differential system and the flow of the linearized system; i.e., H(Φ(t, x0)) = e^(At)H(x0), where A = Df(0) and Φ(t, x0) is the solution of ẋ = f(x), the nonlinear system given by ẋ = -tx.

Theorem 11.11. If X is compact, Y is Hausdorff, and f : X → Y is a continuous bijection, then f is a homeomorphism.

(Topology of the solid torus) A solid torus V is homeomorphic t... | Filo