Linearization via the Lie Derivative
by Carmen Chicone, Richard Swanson
Publisher: American Mathematical Society 2000
Number of pages: 64
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.
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by William F. Trench - Brooks Cole
This text has been written in clear and accurate language that students can read and comprehend. The author has minimized the number of explicitly state theorems and definitions, in favor of dealing with concepts in a more conversational manner.
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These notes contain various versions of the contraction mapping principle. Several applications to existence theorems in differential and integral equations and variational inequalities are given. Also discussed are Hilbert's projective metric.
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Some examples of simple differential equations. The book covers separation of variables, linear differential equation of first order, the existence and uniqueness theorem, the Bernoulli differential equation, and the setup of model equations.
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