arXiv:2604.18202 · v2

Locally invariant manifolds and foliations

首次提交 2026-04-20 20:51

版本更新 2026-10-27 05:05

雷达观测 2026-10-29 00:35

摘要

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.

作者备注：Entirely rewritten since previous version. New version includes more results and more efficient proofs