| Improvement of Hartman's linearization theorem |
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| 作者姓名： | 史金麟 |
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| 作者单位： | Department of |
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| 基金项目： | This work was supported by Fujian Educational Science Foundation (Grant No. K20009). |
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| 摘 要： | Hartman's linearization theorem tells us that if matrix A has no zero real part and f(x) is bounded and satisfies Lipchitz condition with small Lipchitzian constant, then there exists a homeomorphism of Rn sending the solutions of nonlinear system x' = Ax + f(x) onto the solutions of linear system x = Ax. In this paper, some components of the nonlinear item f(x) are permitted to be unbounded and we prove the result of global topological linearization without any special limitation and adding any condition. Thus, Hartman's linearization theorem is improved essentially.
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Improvement of Hartman’s linearization theorem |
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| Jinlin?Shi.Improvement of Hartman''''s linearization theorem[J].Science in China(Mathematics),2003,46(2):215-228. |
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| Authors: | Jinlin Shi |
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| Institution: | Department of Mathematics, Fuzhou University, Fuzhou 350002, China |
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| Abstract: | Hartman's linearization theorem tells us that if matrix A has no zero real part and f(x) is bounded and satisfies Lipchitz condition with small Lipchitzian constant, then there exists a homeomorphism of Rn sending the solutions of nonlinear system x' = Ax + f(x) onto the solutions of linear system x = Ax. In this paper, some components of the nonlinear item f(x) are permitted to be unbounded and we prove the result of global topological linearization without any special limitation and adding any condition. Thus, Hartman's linearization theorem is improved essentially. |
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| Keywords: | linearization theorem improvement |
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