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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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發(fā)表于 2025-3-21 16:44:19 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Normally Hyperbolic Invariant Manifolds
副標(biāo)題The Noncompact Case
編輯Jaap Eldering
視頻videohttp://file.papertrans.cn/669/668077/668077.mp4
概述A gentle introduction: examples, history, overview of methods.Bridges nonlinear dynamics and differential geometry.Includes various new results in bounded geometry.Completely worked out persistence pr
叢書名稱Atlantis Studies in Dynamical Systems
圖書封面Titlebook: Normally Hyperbolic Invariant Manifolds; The Noncompact Case Jaap Eldering Book 2013 Atlantis Press and the author 2013 Bounded geometry.Dy
描述.This monograph treats normally hyperbolic invariant manifolds, with a focus on noncompactness. These objects generalize hyperbolic fixed points and are ubiquitous in dynamical systems..First, normally hyperbolic invariant manifolds and their relation to hyperbolic fixed points and center manifolds, as well as, overviews of history and methods of proofs are presented. Furthermore, issues (such as uniformity and bounded geometry) arising due to noncompactness are discussed in great detail with examples..The main new result shown is a proof of persistence for noncompact normally hyperbolic invariant manifolds in Riemannian manifolds of bounded geometry. This extends well-known results by Fenichel and Hirsch, Pugh and Shub, and is complementary to noncompactness results in Banach spaces by Bates, Lu and Zeng. Along the way, some new results in bounded geometry are obtained and a framework is developed to analyze ODEs in a differential geometric context..Finally, the main result is extended to time and parameter dependent systems and overflowing invariant manifolds..
出版日期Book 2013
關(guān)鍵詞Bounded geometry; Dynamical systems; Noncompactness; Normally hyperbolic invariant manifolds; Persistenc
版次1
doihttps://doi.org/10.2991/978-94-6239-003-4
isbn_softcover978-94-6239-042-3
isbn_ebook978-94-6239-003-4Series ISSN 2213-3526 Series E-ISSN 2213-3534
issn_series 2213-3526
copyrightAtlantis Press and the author 2013
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Jaap Elderingand function of the original organ, a process called .. By contrast, the unimpaired response to severe injury in adult mammals is an irreversible . process leading to closure of the injured site by contraction and formation of scar, a nonphysiological tissue. The consequences of irreversible healing
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Jaap Elderingment, and how this standard therapeutic modality impacts on wound bed preparation. Importantly, wound bed preparation is revolutionizing the way we approach nonhealing or difficult to heal wounds. Much of what we do clinically, from elimination of bacterial burden, to debridement, and to the use of
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Manifolds of Bounded Geometry,ct case to a noncompact setting. We redevelop various technical tools in the context of bounded geometry on Riemannian manifolds, such as a tubular neighborhood and smooth approximation of a submanifold embedding. We also explicitly work out the relation between curvature and holonomy for later use.
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Persistence of Noncompact NHIMs,general version of the main theorem and discuss these in full detail. We include a precise comparison with results in the literature, followed by an outline of the proof. Then we discuss the differences to the compact case and present detailed examples to illustrate these. To start the actual proof,
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