\(n\)-dimensional stable and unstable manifolds of hyperbolic singular point. (English) Zbl 1142.37321

Summary: Invariant manifold play an important role in the qualitative analysis of dynamical systems, such as in studying homoclinic orbit and heteroclinic orbit. This paper focuses on stable and unstable manifolds of hyperbolic singular points. For a type of \(n\)-dimensional quadratic system, such as Lorenz system, Chen system, Rössler system if \(n = 3\), we provide the series expression of manifolds near the hyperbolic singular point, and proved its convergence using the proof of the formal power series. The expressions can be used to investigate the heteroclinic orbits and homoclinic orbits of hyperbolic singular points.


37D10 Invariant manifold theory for dynamical systems
37C29 Homoclinic and heteroclinic orbits for dynamical systems


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