Asymptotic phase for flows with exponentially stable partially hyperbolic invariant manifolds
نویسندگان
چکیده
We consider an autonomous system admitting invariant manifold M. The following questions are discussed: (i) what the conditions ensuring exponential stability of manifold? (ii) does every motion attracting by M tend to some on (i.e. have asymptotic phase)? (iii) is geometrical structure set formed orbits approaching a given orbit? get answer in terms Lyapunov functions omitting assumption that normal bundle trivial. An affirmative obtained for with partially hyperbolic tangent bundle. In this case, existence phase under new involving contraction rates linearized flow and tangential directions. To question (iii), we show neighborhood has foliation each leaf which corresponds motions common phase. contrast theory cascades, our technique exploits classical Lyapunov–Perron method integral equations.
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ژورنال
عنوان ژورنال: Electronic Journal of Qualitative Theory of Differential Equations
سال: 2021
ISSN: ['1417-3875']
DOI: https://doi.org/10.14232/ejqtde.2021.1.36