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Series on Applied and Computational Mathematics, 2021
Peter De Maesschalck +2 more
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Peter De Maesschalck +2 more
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One-Dimensional Center Manifolds are C∞
Results in Mathematics, 1992 It 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.
Aulbach, Bernd (Prof.)
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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.
Boumediene Hamzi +2 more
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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.
Boumediene Hamzi +2 more
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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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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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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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Theory of Invariant Manifold and Foliation and Uniqueness of Center Manifold Dynamics
Journal of Dynamics and Differential Equations, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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Centers on center manifolds in the Lorenz, Chen and Lü systems
Communications in Nonlinear Science and Numerical Simulation, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Antonio Algaba +3 more
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Center Manifolds for Homoclinic Solutions
Journal of Dynamics and Differential Equations, 2000Preprint: Weierstraß-Institut für Angewandte Analysis und Stochastik, vol ...
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