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 Invariant manifolds and invariant foliations are the core research objects in differentiable dynamical systems. They have important applications in the problems of normal form, bifurcation, stable ergodicity and so on. In this talk, we will discuss how to find smooth invariant manifolds and invariant foliations without spectral gap or bunching condition, where the classical graph transformation method and Lapunov-Perron method cannot be used.