Titlebook: Normally Hyperbolic Invariant Manifolds; The Noncompact Case Jaap Eldering Book 2013 Atlantis Press and the author 2013 Bounded geometry.Dy

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n focuses are (1) DPN, which is the main initiating factor for foot ulceration and a cause of troublesome chronic painful neuropathic symptoms, and (2) autonomic neuropathy, often associated with DPN that can involve almost all the systems of the body and may have devastating consequences, such as sudden death.

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tes and determine the success of therapeutic interventions. This chapter will summarize these methods used to assess the cutaneous microcirculation while also describing the respective roles of hyperglycemia, insulin resistance, and inflammation in endothelial dysfunction and its complex relationship with neurovascular function.

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Introduction, geometry and a precise statement of the main result of this work and discuss its relation to the literature. We describe a few extensions and details of the results and conclude the chapter with notation used throughout this book.

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Persistence of Noncompact NHIMs, we first prepare the system: we put it in a suitable form and obtain estimates for the perturbed system. Then we prove that there exists a unique persistent invariant manifold and that it is Lipschitz. Secondly, we set up an elaborate scheme in to prove that this manifold is smooth by induction over the smoothness degree.

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Manifolds of Bounded Geometry,ighborhood and smooth approximation of a submanifold embedding. We also explicitly work out the relation between curvature and holonomy for later use. Finally we use these tools to show how to reduce the main persistence theorem to a setting in a trivial bundle.

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