Construction of Center Manifolds | Zendy

Knobloch H. W. | Zendy

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Construction of Center Manifolds

Author(s) -

Knobloch H. W.

Publication year - 1990

Publication title -

zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 51

eISSN - 1521-4001

pISSN - 0044-2267

DOI - 10.1002/zamm.19900700702

Subject(s) - center manifold , mathematics , manifold (fluid mechanics) , center (category theory) , pure mathematics , invariant manifold , invariant (physics) , boundary (topology) , mathematical analysis , differential topology , combinatorics , ricci flat manifold , geometry , physics , mathematical physics , crystallography , quantum mechanics , nonlinear system , engineering , mechanical engineering , chemistry , hopf bifurcation , scalar curvature , curvature , bifurcation

Given a pair of coupled differential equations ẋ = g(x, y), ẏ = h(x, y), x, y being vectors. The paper is concerned with existence and properties of invariant manifolds given in the form y = S(x), × ∈ M. The questions raised and partially answered differ from the standard content of center manifold theory in two respects. (i) The scenario is non‐local, i.e. the set M is not necessarily small. (ii) The manifold is supposed to satisfy side conditions, namely a boundary condition (S(x) = s(x) for × ∈ ∂M) and condition of inner stability (“inflowing”).

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