On the quantitative estimates of the remainder in normal forms
| Autor: | Ollé Torner, Mercè, Pacha Andújar, Juan Ramón, Villanueva Castelltort, Jordi |
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| Přispěvatelé: | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions |
| Jazyk: | angličtina |
| Rok vydání: | 2002 |
| Předmět: |
Differential equations
Bifurcació Teoria de la 34 Ordinary differential equations::34C Qualitative theory [Classificació AMS] Hamilton Sistemes de 37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory [Classificació AMS] normal forms Bifurcation theory 37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian Lagrangian contact and nonholonomic systems [Classificació AMS] Equacions diferencials ordinàries Hamiltonian systems bounds of the remainder |
| Zdroj: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) Recercat. Dipósit de la Recerca de Catalunya instname |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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