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On the quantitative estimates of the remainder in normal forms
Ollé Torner, Mercè; Pacha Andújar, Juan Ramón; Villanueva Castelltort, Jordi
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
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.
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
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
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