caa a22 4500 47709144X CHVBK 20180405111516.0 cr unu---uuuuu 170330e19960301xx s 000 0 eng 10.1007/BF01194215 doi (NATIONALLICENCE)springer-10.1007/BF01194215 Global center manifolds in singular systems [Elektronische Daten] [Flaviano Battelli, Michal Fečkan] The problem of existence of aglobal center manifold for a system of O.D.E. like (*) $$\left\{ {\begin{array}{*{20}c} {\dot x = A(y)x + F(x,y)} \\ {\dot y = G(x,y), (x,y) \in \mathbb{R}^n \times \mathbb{R}^m ,} \\ \end{array} } \right.$$ is considered. We give conditions onA(y), F(x, y), G(x, y) in order that a functionH: ℝ m →ℝ n , with the same smoothness asA(y), F(x, y), G(x, y), exists and is such that the manifoldC={(x,y)∈ℝ n ×ℝ m ∣x=H(y),y∈ℝ m } is an invariant manifold for (*), and there exists ρ>0 such that any solution of (*) satisfying sup t∈ℝ∣x(t)∣ <ρ must belong toC. This is why we callC global center manifold. Applications are given to the problem of existence of heteroclinic orbits in singular systems. Birkhäuser Verlag, 1996 Battelli Flaviano Dipartimento di Energetica, Facoltà di Ingegneria-Università, 67040, Monteluco Roio L'Aquila, Italy aut Fečkan Michal Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia aut Nonlinear Differential Equations and Applications NoDEA Birkhäuser-Verlag 3/1(1996-03-01), 19-34 1021-9722 3:1<19 1996 3 30 https://doi.org/10.1007/BF01194215 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01194215 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Battelli Flaviano Dipartimento di Energetica, Facoltà di Ingegneria-Università, 67040, Monteluco Roio L'Aquila, Italy aut NATIONALLICENCE 700 1- Fečkan Michal Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Birkhäuser-Verlag 3/1(1996-03-01), 19-34 1021-9722 3:1<19 1996 3 30 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer