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Smooth invariant manifolds and foliations without a spectral gap
张文萌教授(重庆师范大学)
2018年10月15日(星期一)13:00-14:00  闵行数学楼126报告厅

报告摘要:It is known that a spectral gap condition is required for the existence and smoothness of invariant manifolds and invariant foliations near a fixed point. However, any planar mapping with a unipotent linear part, having a center manifold on the whole phase plane, does not have such a gap. In this talk, we give the existence and smoothness of invariant manifolds, which are invariant submanifolds of the center manifold, for the aforementioned planar mapping. Corresponding to the invariant submanifolds, we further give the existence and smoothness of invariant foliations on the center manifold.