The stable, center-stable, center, center-unstable, unstable manifolds

Keywords

Center (category theory), Mathematics, Center manifold, Ordinary differential equation, Smoothness

References

• Perturbation theorems for periodic surfacesStephen P. Diliberto — 1958
• Problème général de la stabilité du mouvementA. M. Li︠a︡punov — 1949
• Vorlesungen über HimmelsmechanikCarl Ludwig Siegel — 1956
• On the Liapounov subcenter manifoldAl Kelley — 1967
• Stability of the center-stable manifoldAl Kelley — 1967
• Asymptotic methods in the theory of non-linear oscillationsN. DeClaris — 1963
• Perturbation theorems for periodic surfaces I—Definitions and main theoremsStephen P. Diliberto — 1960
• A New Approach to the Perturbation Theory of Invariant SurfacesRobert J. Sacker — 1965
• INTEGRAL MANIFOLDS OF PERTURBED DIFFERENTIAL SYSTEMSJack K. Hale — 1961
• Small Periodic Pertubations of an Autonomous System with a Stable OrbitNorman Levinson — 1950
• Problème général de la stabilité du mouvementAlexandr Mikhailovich Liapounoff — 1907
• Asymptotic Methods in the Theory of Non-Linear OscillationsN. N. Bogoli︠u︡bov, Y. A. Mitropolski — 1961

Cited by

• Controlling nonuniqueness of local invariant manifolds.Pavol Brunovský — 1994
• Smoothness of unordered curves in two-dimensional strongly competitive systemsJanusz Mierczyński — 1999
• Formes normales de champs de vecteurs : restes exponentiellement petits dans le cas non autonomeTiphaine Jézéquel — 2011
• Genetic engineering via negative fitness:Evolutionary dynamics for global optimizationImmanuel M. Bomze, Volker Stix — 1999
• Nonautonomous Dynamical SystemsPeter E. Kloeden, Martin Rasmussen — 2011
• О проблемах теории термина на симпозиумах Германского терминологического конгрессаВ.А. Татаринов — 1995
• Periodikus funkcionál-differenciálegyenletek bifurkációelméleteGergely Röst — 2006
• Centre manifolds for infinite dimensional random dynamical systemsXiaopeng Chen, A. J. Roberts, Jinqiao Duan — 2013
• Regularity of Center Manifolds via the Graph TransformBjörn Sandstede, Thunwa Theerakarn — 2015
• Stability Analysis of Singularly Perturbed Systems using Slow and Fast ManifoldsKwok W. Cheung, Joe H. Chow — 1991
• Center manifold and stability in critical cases for some partial functional differential equationsMostafa Adimy, Khalil Ezzinbi, Wu, Jianhong — 2006
• Axisymmetric solutions of the Chaplygin gas for initial negative radial velocityLihui Guo, Wancheng Sheng — 2010
• Axisymmetric Solutions of the Euler Equations for Sub-Square Polytropic GasesYuxi Zheng, Tong Zhang — 1998
• Lectures on Analytic Differential EquationsYu. Ilyashenko, Sergeî Yakovenko — 2007
• Control of center manifoldsBoumediene Hamzi, Wei Kang, Arthur J. Krener — 2003
• Slow Manifold Simulation of Power SystemsKwok W. Cheung, Joe H. Chow — 1992
• Methods of qualitative theory in nonlinear dynamicsL. P. Shilnikov, Andrey Shilnikov, Dmitry Turaev — 1998
• Applications of singularity theory to neurobiology.Isabel S. Labouriau — 1983
• A Critical Centre-Stable Manifold for Schroedinger's Equation in R^3Marius Beceanu — 2009
• Local Stable Manifold for the Bidirectional Discrete-Time DynamicsCarmeliza Navasca — 2003

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