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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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Center manifold of unstable periodic orbits of helium atom: numerical evidence
Discrete and Continuous Dynamical Systems - Series B, 2003 An original numerical method is introduced for the calculation of orbits on the center manifold of an unstable periodic orbit. The method is implemented for some unstable periodic orbits of the helium atom, and the dynamics on the corresponding center ...
A Carati
exaly +1 more source
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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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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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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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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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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