Normally Hyperbolic Invariant Manifolds in Dynamical SystemsSpringer Science & Business Media, 10 jun 1994 - 194 páginas In the past ten years, there has been much progress in understanding the global dynamics of systems with several degrees-of-freedom. An important tool in these studies has been the theory of normally hyperbolic invariant manifolds and foliations of normally hyperbolic invariant manifolds. In recent years these techniques have been used for the development of global perturbation methods, the study of resonance phenomena in coupled oscillators, geometric singular perturbation theory, and the study of bursting phenomena in biological oscillators. "Invariant manifold theorems" have become standard tools for applied mathematicians, physicists, engineers, and virtually anyone working on nonlinear problems from a geometric viewpoint. In this book, the author gives a self-contained development of these ideas as well as proofs of the main theorems along the lines of the seminal works of Fenichel. In general, the Fenichel theory is very valuable for many applications, but it is not easy for people to get into from existing literature. This book provides an excellent avenue to that. Wiggins also describes a variety of settings where these techniques can be used in applications. |
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Normally Hyperbolic Invariant Manifolds in Dynamical Systems Stephen Wiggins Vista previa restringida - 2013 |
Normally Hyperbolic Invariant Manifolds in Dynamical Systems Stephen Wiggins No hay ninguna vista previa disponible - 2013 |
Normally Hyperbolic Invariant Manifolds in Dynamical Systems Stephen Wiggins No hay ninguna vista previa disponible - 2013 |
Términos y frases comunes
asymptotic At(p basepoint Bt(p center manifold consider construction contraction mapping coordinate chart Cr diffeomorphism Cr manifold defined definition denote derivative diffeomorphism differentiable manifold dynamical systems exists Fenichel fiber foliation function geometrical given GR-I estimates graph transform Hamiltonian Hence hij f1(z hyperbolic fixed point inequality inflowing invariant IR³ linearized dynamics Lipschitz Lyapunov-type numbers M₁ manifold with boundary metric neighborhood nonlinear norm normal bundle normally hyperbolic notation obtain open set orbits ordinary differential equations overflowing invariant manifold persistence theorem phase space proof Proposition stable and unstable sufficiently small tangent bundle tangent space theorem for overflowing Theory time-T map trajectories uniformity lemma unstable manifold theorem uz(x vector field vector space Wiggins Wu(M
Pasajes populares
Página 186 - Falzarano, J., Shaw, S and Troesch, A (1992)," Application of Global Methods for Analyzing Dynamical systems to Ship Rolling Motion and Capsizing, Journal of Bifurcation and Chaos, Vol.