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arXiv · 2512.22062

Existence of spectral submanifolds in time delay systems

Gergely Buza·George Haller
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Abstract

Spectral submanifolds (SSMs) are invariant manifolds of a dynamical system, defined by the property of being tangent to a spectral subspace of the linearized dynamics at a steady state. We show existence, along with certain desirable properties such as smoothness, attractivity and conditional uniqueness, of SSMs associated to a large class of spectral subspaces in time delay systems. Building on these results, we generalize the criteria for existence of inertial manifolds -- defined as globally exponentially attracting Lipschitz invariant manifolds of finite dimension -- and show that they need not have dimension equal to that of the physical configuration, in contrast to previous accounts. We then demonstrate the applicability of these results on a few simple examples.

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Gergely Buza, George Haller. 2025-12-26. Existence of spectral submanifolds in time delay systems. https://arxiv.org/abs/2512.22062

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