Downloads provided by UsageCountsOn the quantitative estimates of the remainder in normal forms
Ollé Torner, Mercè; Pacha Andújar, Juan Ramón; Villanueva Castelltort, Jordi;
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) 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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Differential equations, Teoria de la, Classificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory, Bifurcació, Teoria de la, :34 Ordinary differential equations::34C Qualitative theory [Classificació AMS], Classificació AMS::34 Ordinary differential equations::34C Qualitative theory, :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 [Classificació AMS], Bifurcació, Sistemes de, Hamilton, Sistemes de, normal forms, Bifurcation theory, Hamilton, Equacions diferencials ordinàries, and nonholonomic systems, Hamiltonian systems, Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems, bounds of the remainder, Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact
Differential equations, Teoria de la, Classificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory, Bifurcació, Teoria de la, :34 Ordinary differential equations::34C Qualitative theory [Classificació AMS], Classificació AMS::34 Ordinary differential equations::34C Qualitative theory, :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 [Classificació AMS], Bifurcació, Sistemes de, Hamilton, Sistemes de, normal forms, Bifurcation theory, Hamilton, Equacions diferencials ordinàries, and nonholonomic systems, Hamiltonian systems, Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems, bounds of the remainder, Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact
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