版本更新 · v2arXiv:2604.18202
Locally invariant manifolds and foliations
Lachlan Ewen MacDonald
Invariant manifolds and foliations associated to invariant pseudo-hyperbolic reference geometries have been well-studied in the context of dynamics implemented by a diffeomorphism. In this paper, we provide sufficient conditions for the existence of maximally smooth, \emph{locally} invariant manifolds and foliations containing a given \emph{locally} invariant, pseudo-hyperbolic reference geometry, in the context of dynamics implemented by a smooth map which need not be invertible. The theory is motivated by applications to the developing theory of large-step optimisation.
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math.DS · cs.LG