Linearization via the Lie Derivative
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Description: By Carmen Chicone and Richard Swanson. LaTeX, DVI, PostScript and PDF.
Electronic Journal of Differential Equations Electron. J. Diff. Eqns., Monograph 02, 2000. Linearization via the Lie Derivative Carmen Chicone & Richard Swanson The standard proof of the Grobman--Hartman linearization theorem for a flow at a hyperbolic rest point proceeds by first establishing the analogous result for hyperbolic fixed points of local diffeomorphisms. In this exposition we present a simple direct proof that avoids the discrete case altogether. We give new proofs for Hartman's smoothness results: A flow is linearizable at a hyperbolic sink, and a flow in the plane is linearizable at a hyperbolic rest point. Also, we formulate and prove some new results on smooth linearization for special classes of quasi-linear vector fields where either the nonlinear part is restricted or additional conditions on the spectrum of the linear part (not related to resonance conditions) are imposed.
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| Page title: | Electronic Journal of Differential Equations |
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| NS | Name Servers: NS5.TXSTATE.EDU 147.26.8.202 NS6.TXSTATE.EDU 147.26.8.203 |
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| Date | activated: 09-Jul-2003 last updated: 23-May-2012 expires: 31-Jul-2014 |