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1976
In this section we will start to carry out the program outlined in Section 1 by proving the center manifold theorem. The general invariant manifold theorem is given in Hirsch-Pugh-Shub [1]. Most of the essential ideas are also in Kelley [1] and a treatment with additional references is contained in Hartman [1]. However, we shall follow a proof given by
J. E. Marsden, M. McCracken
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In this section we will start to carry out the program outlined in Section 1 by proving the center manifold theorem. The general invariant manifold theorem is given in Hirsch-Pugh-Shub [1]. Most of the essential ideas are also in Kelley [1] and a treatment with additional references is contained in Hartman [1]. However, we shall follow a proof given by
J. E. Marsden, M. McCracken
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On the stability of the center manifold
ZAMP Zeitschrift f�r angewandte Mathematik und Physik, 1987A new lemma in the theory of center manifolds is proved with the help of Gronwall's inequality. It means that as long as a trajectory of the dynamical system remains in a neighborhood of a singular point with given center manifold, it must be close to some trajectory on the mentioned manifold.
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2010
This chapter provides a systematic technique for designing center manifold of closed loop of nonlinear systems to stabilize the system. The method was firstly presented in [6]. Section 11.1 introduces some fundamental concepts and results about center manifold theory. Section 11.2 considers the case when the zero dynamics has minimum phase.
Daizhan Cheng, Xiaoming Hu, Tielong Shen
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This chapter provides a systematic technique for designing center manifold of closed loop of nonlinear systems to stabilize the system. The method was firstly presented in [6]. Section 11.1 introduces some fundamental concepts and results about center manifold theory. Section 11.2 considers the case when the zero dynamics has minimum phase.
Daizhan Cheng, Xiaoming Hu, Tielong Shen
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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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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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The Grassmann-like Manifold of Centered Planes
Mathematical Notes, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Center manifolds for ill-posed stochastic evolution equations
Discrete and Continuous Dynamical Systems - Series B, 2022Caibin Zeng, Zonghao Li
exaly
The center problem on a center manifold in
Nonlinear Analysis: Theory, Methods & Applications, 2012Victor F. Edneral +3 more
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