3 papers
math.CA2025
Stable invariant manifold for generalized ODEs with applications to measure differential equations
Weijie Lu, Paolo Piccione, Yonghui Xia
This paper establishes the stable invariant manifold for a new kind of differential equations defined by Kurzweil integral, so-called {\em generalized ODEs} on a Banach space. The…
math.DS2025
Pugh's global linearization for the nonautonomous unbounded system with -dichotomy via Lyapunov theory
Weijie Lu, Yonghui Xia
The classical global linearization theorem for autonomous system given in [C. Pugh, Amer. J. Math., 91 (1969) 363-367] requires that nonlinear system with hyperbolicity satisfies b…
math.CA2023
Linearization and Hölder continuity of generalized ODEs with application to measure differential equations
Weijie Lu, Yonghui Xia
In this paper, we study the topological conjugacy between the linear generalized ODEs (for short, GODEs) \[ \frac{dx}{dτ}=D[A(t)x] \] and their nonlinear perturbation \[ \frac{dx}{…