Electron. J. Diff. Eqns., Monograph 02, 2000.
Linearization via the Lie Derivative
Carmen Chicone & Richard Swanson
Abstract:
The standard proof of the GrobmanHartman 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 quasilinear 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.
Submitted November 14, 2000. Published December 4, 2000.
Math Subject Classifications: 3402, 34C20, 37D05, 37G10.
Key Words: Smooth linearization, Lie derivative, Hartman, Grobman,
hyperbolic rest point, fiber contraction, Dorroh smoothing.
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Carmen Chicone
Department of Mathematics
University of Missouri
Columbia, MO 65211, USA
email: carmen@chicone.math.missouri.edu 

Richard Swanson
Department of Mathematical Sciences
Montana State University,
Bozeman, MT 597170240, USA
email: rswanson@math.montana.edu

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