7 papers
Differentiable normal linearization of partially hyperbolic dynamical systems
Weijie Lu, Yonghui Xia, Weinian Zhang +1
A result on linearization which is differentiable at the hyperbolic fixed point is known. In this paper, we further investigate a partially hyperbolic diffeomorphism to f…
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…
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…
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}{…
Higher regularity of homeomorphisms in the Hartman-Grobman theorem and a conjecture on its sharpness
Weijie Lu, Manuel Pinto, Y-H Xia
Hartman-Grobman theorem states that there is a homeomorphism H sending the solutions of the nonlinear system onto those of its linearization under suitable assumptions. Many mathem…
Sharpness of conjugacy for the non-autonomous differential equations with Lipschitzian perturbation
Weijie Lu, Manuel Pinto, Y-H. Xia
The classical linearization theorem for the non-autonomous differential equations states the existence of a topological conjugacy between the nonlinear system and its l…
Higher regularity of homeomorphisms in the Hartman-Grobman theorem for semilinear evolution equations
Weijie Lu, Manuel Pinto, Y. H Xia
Hein and Prüss [J. Differential Equations, 261(2016)4709-4727] presented a version of Hartman-Grobman type linearization result for semilinear hyperbolic evolution equation…