Properties of Center Manifolds

DOI10.2307/2000247zbMath0577.34039OpenAlexW4237539362MaRDI QIDQ3699190

Jan Sijbrand

Publication date: 1985

Full work available at URL: https://doi.org/10.2307/2000247

zbMATH Keywords

existencedifferentiabilityuniquenessanalyticitycenter manifolds

Mathematics Subject Classification ID

Related Items (60)

Regularity of center manifolds via the graph transform ⋮ Center manifolds and contractions on a scale of Banach spaces ⋮ Initial conditions for models of dynamical systems ⋮ Local bifurcations of continuous dynamical systems under higher order conditions ⋮ Nonlinear Controller Design Based on Invariant Manifold Theory ⋮ Geometric chaos indicators and computations of the spherical hypertube manifolds of the spatial circular restricted three-body problem ⋮ Singular initial value problems for scalar quasi-linear ordinary differential equations ⋮ Center manifolds for infinite dimensional nonautonomous differential equations ⋮ Numerical study of the geometry of the phase space of the Augmented Hill Three-Body problem ⋮ Conjugate dynamics on center-manifolds for stochastic partial differential equations ⋮ Lower bounds for the cyclicity of centers of quadratic three-dimensional systems ⋮ The center problem on a center manifold in \(\mathbb{R}^{3}\) ⋮ Desynchronization and inhibition of Kuramoto oscillators by scalar mean-field feedback ⋮ Theory of invariant manifold and foliation and uniqueness of center manifold dynamics ⋮ Existence of inverse Jacobi multipliers around Hopf points in \(\mathbb R^3\): emphasis on the center problem ⋮ Cyclicity of rigid centres on centre manifolds of three-dimensional systems ⋮ Reduction of a tri-modal Lorenz model of ferrofluid convection to a cubic-quintic Ginzburg-Landau equation using the center manifold theorem ⋮ Center manifolds for delay-differential equations with variable argument ⋮ BIFURCATION THEORY OF FUNCTIONAL DIFFERENTIAL EQUATIONS: A SURVEY ⋮ Nilpotent centers from analytical systems on center manifolds ⋮ Properties of monodromic points on center manifolds in \(\mathbb R^3\) via Lie symmetries ⋮ Inverse Jacobian multipliers and Hopf bifurcation on center manifolds ⋮ Time dependent center manifold in PDEs ⋮ Choose inter-element coupling to preserve self-adjoint dynamics in multiscale modelling and computation ⋮ On the existence and uniqueness of solutions to the output regulation equations for periodic exosystems ⋮ Meso-scale obstructions to stability of 1D center manifolds for networks of coupled differential equations with symmetric Jacobian ⋮ Limit Cycles in a Model of Olfactory Sensory Neurons ⋮ Solution of the Lorenz Model with Help from the Corresponding Ginzburg-Landau Model ⋮ Smoothness of invariant manifolds ⋮ A complete renormalization group trajectory between two fixed points ⋮ On the hydrodynamics of biaxial nematic liquid crystals. I: General theory ⋮ One-dimensional center manifolds are \(C^{\infty{}}\) ⋮ A hybrid symbolic-numerical approach to the center-focus problem ⋮ Numerical Computation of Periodic Orbits and Isochrons for State-Dependent Delay Perturbation of an ODE in the Plane ⋮ Arnold's mechanism of diffusion in the spatial circular restricted three-body problem: A semi-analytical argument ⋮ Centers on center manifolds in the Lü system ⋮ The invariant manifold of beam deformations. I: The simple circular rod ⋮ Center manifolds theorem for parameterized delay differential equations with applications to zero singularities ⋮ Investigation of center manifolds of three-dimensional systems using computer algebra ⋮ Structural stability under conditions of nonhyperbolicity ⋮ Periodic and quasi-periodic motions of a solar sail close to \(SL _{1}\) in the Earth-Sun system ⋮ Cyclicity of polynomial nondegenerate centers on center manifolds ⋮ Hopf bifurcations in a predator-prey model with an omnivore ⋮ Families of Halo-like invariant tori around \(L_2\) in the Earth-Moon bicircular problem ⋮ A smooth center manifold theorem which applies to some ill-posed partial differential equations with unbounded nonlinearities ⋮ Global Persistence of Lyapunov Subcenter Manifolds as Spectral Submanifolds under Dissipative Perturbations ⋮ Stable manifolds to bounded solutions in possibly ill-posed PDEs ⋮ A dynamical systems approach for the contact-line singularity in thin-film flows ⋮ Linearizing the expanding part of noninvertible mappings ⋮ Bifurcations of continuous dynamical systems under extreme and new transversality conditions ⋮ A center manifold for second order semilinear differential equations on the real line and applications to the existence of wave trains for the Gurtin–McCamy equation ⋮ Center manifolds for semilinear equations with non-dense domain and applications to Hopf bifurcation in age structured models ⋮ Patchy solution of a Francis-Byrnes-Isidori partial differential equation ⋮ Parameterization Method for State-Dependent Delay Perturbation of an Ordinary Differential Equation ⋮ No Chaos in Dixon’s System ⋮ Bifurcations and nondegenerated conditions of higher degree and a new simple proof of the Hopf-Neimark-Sacker bifurcation theorem ⋮ Center manifolds for smooth invariant manifolds ⋮ ``Test two, choose the better leads to high cooperation in the centipede game ⋮ Cusp and generalized flip bifurcations under higher degree conditions ⋮ Regularization of sliding global bifurcations derived from the local fold singularity of Filippov systems

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