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Construction of Center Manifolds
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1990AbstractGiven a pair of coupled differential equations ẋ = g(x, y), ẏ = h(x, y), x, y being vectors. The paper is concerned with existence and properties of invariant manifolds given in the form y = S(x), × ∈ M. The questions raised and partially answered differ from the standard content of center manifold theory in two respects.
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42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), 2004
In this paper, we use a feedback to change the orientation and the shape of the center manifold of a system with uncontrollable linearization. This change directly affect the reduced dynamics on the center manifold, and hence change the stability properties of the original system.
B. Hamzi, null Wei Kang, A.J. Krener
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In this paper, we use a feedback to change the orientation and the shape of the center manifold of a system with uncontrollable linearization. This change directly affect the reduced dynamics on the center manifold, and hence change the stability properties of the original system.
B. Hamzi, null Wei Kang, A.J. Krener
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1995
In this chapter we analyse the behaviour of the nonlinear semiflow near a nonhyperbolic equilibrium; that is, we consider the situation where A does have spectrum on the imaginary axis. We use the decomposition of X as $$X\, = {X_ - } \oplus {X_0} \oplus {X_{ + \cdot }}$$
Odo Diekmann +3 more
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In this chapter we analyse the behaviour of the nonlinear semiflow near a nonhyperbolic equilibrium; that is, we consider the situation where A does have spectrum on the imaginary axis. We use the decomposition of X as $$X\, = {X_ - } \oplus {X_0} \oplus {X_{ + \cdot }}$$
Odo Diekmann +3 more
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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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Nonlinear Analysis: Theory, Methods & Applications, 1997
Let \(X\) be a Banach space. Consider the semiflow \(\Phi:X\to X\) with \(\Phi(x) =U(x)+ g(x)\), \(U\in L(X,X)\), \(g\in C^k(X,X)\), \(k\geq 1\), \(g(0)=0\).
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Let \(X\) be a Banach space. Consider the semiflow \(\Phi:X\to X\) with \(\Phi(x) =U(x)+ g(x)\), \(U\in L(X,X)\), \(g\in C^k(X,X)\), \(k\geq 1\), \(g(0)=0\).
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Isochronicity of centers at a center manifold
AIP Conference Proceedings, 2012For a three dimensional system with a center manifold filled with closed trajectories (corresponding to periodic solutions of the system) we give criteria on the coefficients of the system to distinguish between the cases of isochronous and non-isochronous oscillations. Bifurcations of critical periods of the system are studied as well.
Brigita Ferčec, Matej Mencinger
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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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