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- W2899398471 abstract "The celebrated Hartman-Grobman theorem for ordinary differential equations states that the phase portrait nearby a hyperbolic equilibrium point of a nonlinear system is equivalent to that of its linearization by a conjugation. Hartman and Grobmans theorem has been extended in numerous ways to accommodate more general classes of dynamical systems. For instance, generalizations have been proven for finite-dimensional nonautonomous systems, impulsive systems, and impulsive differential equations in Banach spaces. All of the aforementioned generalized results, however, require global Lipschitz assumptions on the vector field and jump map, as well as intimate knowledge of the dichotomy properties of the linearized system. Since many systems encountered in applied fields are nonlinear and not globally Lipschitz, there is a need to weaken the assumptions. We show that one can localize such linearization theorems near a hyperbolic equilibrium point, provided sufficient smoothness conditions are satisfied and time-varying terms are suitably bounded. Global assumptions on the nonlinearity are no longer necessary and one does not require as detailed an analysis of the linearized system to apply the result." @default.
- W2899398471 created "2018-11-09" @default.
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- W2899398471 date "2018-01-01" @default.
- W2899398471 modified "2023-09-25" @default.
- W2899398471 title "Linearization and Local Topological Conjugacies for Impulsive Systems" @default.
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- W2899398471 doi "https://doi.org/10.1007/978-3-319-99719-3_53" @default.
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