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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…