Blow-up behavior for ODEs with normally hyperbolic nature in dynamics at infinity
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917756908077056 |
|---|---|
| author | Matsue, Kaname |
| author_facet | Matsue, Kaname |
| contents | We describe blow-up behavior for ODEs by means of dynamics at infinity with complex asymptotic behavior in autonomous systems, as well as in nonautonomous systems. Based on preceding studies, a variant of closed embeddings of phase spaces and the time-scale transformation determined by the structure of vector fields at infinity reduce our description of blow-ups to unravel the shadowing property of (pre)compact trajectories on the horizon, the geometric object expressing the infinity, with the specific convergence rates. Geometrically, this description is organized by asymptotic phase of invariant sets on the horizon. Blow-up solutions in nonautonomous systems can be described in a similar way. As a corollary, normally, or partially hyperbolic invariant manifolds on the horizon possessing asymptotic phase are shown to induce blow-ups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_09201 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Blow-up behavior for ODEs with normally hyperbolic nature in dynamics at infinity Matsue, Kaname Dynamical Systems Classical Analysis and ODEs 34A26, 34C08, 34C45, 35B44, 37C60, 37D10, 58K55 We describe blow-up behavior for ODEs by means of dynamics at infinity with complex asymptotic behavior in autonomous systems, as well as in nonautonomous systems. Based on preceding studies, a variant of closed embeddings of phase spaces and the time-scale transformation determined by the structure of vector fields at infinity reduce our description of blow-ups to unravel the shadowing property of (pre)compact trajectories on the horizon, the geometric object expressing the infinity, with the specific convergence rates. Geometrically, this description is organized by asymptotic phase of invariant sets on the horizon. Blow-up solutions in nonautonomous systems can be described in a similar way. As a corollary, normally, or partially hyperbolic invariant manifolds on the horizon possessing asymptotic phase are shown to induce blow-ups. |
| title | Blow-up behavior for ODEs with normally hyperbolic nature in dynamics at infinity |
| topic | Dynamical Systems Classical Analysis and ODEs 34A26, 34C08, 34C45, 35B44, 37C60, 37D10, 58K55 |
| url | https://arxiv.org/abs/2307.09201 |