Linearization and Global Dynamics
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In this paper we show how the spectral theory of linear skew-product flows may be used to study the following three questions in the qualitative theory of dynamical systems: (1) when is an -limit set or an attractor a manifold? (2) Under which conditions will a dynamical system undergo a Hopf-Landau bifurcation from a k-dimensional torus to a (k + 1)-dimensional torus? (3) When is a vector field i the vicinity of a compact invariant manifold smoothly conjugate to the linearized vector field and how smooth is the conjugacy?
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Sell, George R.. (1983). Linearization and Global Dynamics. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/4057.
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