Existence of spectral submanifolds in time delay systems
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909976339939328 |
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| author | Buza, Gergely Haller, George |
| author_facet | Buza, Gergely Haller, George |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22062 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence of spectral submanifolds in time delay systems Buza, Gergely Haller, George Dynamical Systems Chaotic Dynamics 34K19 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. |
| title | Existence of spectral submanifolds in time delay systems |
| topic | Dynamical Systems Chaotic Dynamics 34K19 |
| url | https://arxiv.org/abs/2512.22062 |