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2013
A center manifold at a given nonhyperbolic equilibrium is an invariant manifold of a given differential equation that is tangent at the equilibrium point to the (generalized) eigenspace of the neutrally stable eigenvalues. Since the local dynamic behavior transverse to the center manifold is relatively simple, the potentially complicated asymptotic ...
Shangjiang Guo, Jianhong Wu
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A center manifold at a given nonhyperbolic equilibrium is an invariant manifold of a given differential equation that is tangent at the equilibrium point to the (generalized) eigenspace of the neutrally stable eigenvalues. Since the local dynamic behavior transverse to the center manifold is relatively simple, the potentially complicated asymptotic ...
Shangjiang Guo, Jianhong Wu
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Analytic Center Manifolds of Dimension One
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1986AbstractThe flow of a system of ordinary differential equations near an equilibrium point is completely determined by the flow restricted to a corresponding center manifold. Even for analytic equations center manifolds need not be analytic and therefore, in general, the flow on a center manifold cannot be described by an analytic equation.
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2000
Center manifold theory is essential for analyzing local bifurcations. As the Liapunov-Schmidt reduction for stationary and Hopf bifurcations, center manifold theory is used to reduce a dynamical system near a nonhyperbolic equilibrium or a periodic solution to a low-dimensional system with the vector field as functions of the critical modes ...
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Center manifold theory is essential for analyzing local bifurcations. As the Liapunov-Schmidt reduction for stationary and Hopf bifurcations, center manifold theory is used to reduce a dynamical system near a nonhyperbolic equilibrium or a periodic solution to a low-dimensional system with the vector field as functions of the critical modes ...
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One-Dimensional Center Manifolds are C∞
Results in Mathematics, 1992It is well known that center manifolds of analytic differential equations are not of class C∞ in general. In this paper it is shown that they are indeed C∞ if they are one-dimensional.
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The Grassmann-like Manifold of Centered Planes
Mathematical Notes, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The center problem on a center manifold in
Nonlinear Analysis: Theory, Methods & Applications, 2012Victor F. Edneral +3 more
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