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Title:	On the quantitative estimates of the remainder in normal forms
Author:	Ollé Torner, Mercè; Pacha Andújar, Juan Ramón; Villanueva Castelltort, Jordi
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
Abstract:	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.
Subject(s):	-Hamiltonian systems -Bifurcation theory -Differential equations -Hamiltonian systems -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
Rights:	Attribution-NonCommercial-NoDerivs 2.5 Spain http://creativecommons.org/licenses/by-nc-nd/2.5/es/
Document type:	Article
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