This research reveals stability in pointwise hyperbolic systems, indicating connections to differential dynamical systems.
The stability of the system is an important part of the research on differential dynamical systems. This paper considers a pointwise hyperbolic system defined on a connected open subset N of a compact smooth Riemannian manifold M. The hyperbolicity may weaken when approaching the boundary of the open set. By analogy with the stability of hyperbolic systems, this paper constructs the expansive property and the shadowing lemma on the pointwise pseudo orbits and thus obtains the stability of pointwise hyperbolic systems.
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Guo et al. (2025) studied this question.
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