Kolmogorov Theorem Revisited
Kolmogorov Theorem on the persistence of invariant tori of real analytic Hamiltonian systems is revisited. In this paper we are mainly concerned with the lower bound on the constant of the Diophantine condition required by the theorem. From the existing proofs in the literature, this lower bound tur...
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| Tipo de recurso: | informe técnico |
| Fecha de publicación: | 2004 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/2820 |
| Acceso en línea: | https://hdl.handle.net/2117/2820 |
| Access Level: | acceso abierto |
| Palabra clave: | Ergodic theory Dynamical systems Kolmogorov Theorem Sistemes dinàmics diferenciables Teoria ergòdica Classificació AMS::37 Dynamical systems and ergodic theory Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | Kolmogorov Theorem on the persistence of invariant tori of real analytic Hamiltonian systems is revisited. In this paper we are mainly concerned with the lower bound on the constant of the Diophantine condition required by the theorem. From the existing proofs in the literature, this lower bound turns to be of O(ε1/4), where ε is the size of the perturbation. In this paper, by means of careful (but involved) estimates on Kolmogorov’smethod, we show that this lower bound can be weakened to be of O(ε1/2). This condition coincides with the optimal one of KAM Theorem. Moreover, we also obtain optimal estimates for the distance between the actions of the perturbed and unperturbed tori. |
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