$C^1$ invariant, stable and inertial manifolds for non-autonomous dynamical systems
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915523680272384 |
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| author | Czaja, Radosław Kalita, Piotr Oliveira-Sousa, Alexandre N. |
| author_facet | Czaja, Radosław Kalita, Piotr Oliveira-Sousa, Alexandre N. |
| contents | We use the version of the Lyapunov--Perron method operating on individual solutions to investigate the existence of invariant manifolds for non-autonomous dynamical systems, focusing in particular on inertial and stable manifolds. We establish a characterization of both types of manifolds in terms of solutions exhibiting a common growth behavior, analogous to the classical characterization involving hyperbolicity. Furthermore, we introduce a unified formulation of the gap condition, from which known sharp versions are derived. Finally, we show that the constructed inertial manifolds have $C^1$ regularity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_00165 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $C^1$ invariant, stable and inertial manifolds for non-autonomous dynamical systems Czaja, Radosław Kalita, Piotr Oliveira-Sousa, Alexandre N. Dynamical Systems Analysis of PDEs 37L25, 35B42, 37D10, 37L05, 37L30 We use the version of the Lyapunov--Perron method operating on individual solutions to investigate the existence of invariant manifolds for non-autonomous dynamical systems, focusing in particular on inertial and stable manifolds. We establish a characterization of both types of manifolds in terms of solutions exhibiting a common growth behavior, analogous to the classical characterization involving hyperbolicity. Furthermore, we introduce a unified formulation of the gap condition, from which known sharp versions are derived. Finally, we show that the constructed inertial manifolds have $C^1$ regularity. |
| title | $C^1$ invariant, stable and inertial manifolds for non-autonomous dynamical systems |
| topic | Dynamical Systems Analysis of PDEs 37L25, 35B42, 37D10, 37L05, 37L30 |
| url | https://arxiv.org/abs/2508.00165 |