On the quantitative estimates of the remainder in normal forms
We consider an analytic Hamiltonian system with three degrees of freedom and having a family of periodic orbits with a transition stability complex instability. We reduce the Hamiltonian to a normal form around a transition periodic orbit and we obtain H = Z^r + R^r. The analysis of the (truncated)...
| Authors: | , , |
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| Format: | article |
| Publication Date: | 2002 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/1219 |
| Online Access: | https://hdl.handle.net/2117/1219 |
| Access Level: | Open access |
| Keyword: | Hamiltonian systems Bifurcation theory Differential equations normal forms bounds of the remainder Hamilton, Sistemes de Bifurcació, Teoria de la Equacions diferencials ordinàries Classificació AMS::34 Ordinary differential equations::34C Qualitative theory Classificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems |
| Summary: | We consider an analytic Hamiltonian system with three degrees of freedom and having a family of periodic orbits with a transition stability complex instability. We reduce the Hamiltonian to a normal form around a transition periodic orbit and we obtain H = Z^r + R^r. The analysis of the (truncated) normal form, Z^r, allows the description of a Hopf bifurcation of 2D-tori. However, this communication will concentrate on the study of the remainder, R^r and some comparison between the remainder obtained when considering the normal form around an elliptic equilibrium point and around a critical periodic orbit will be made. |
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