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Dynamics and bifurcation near the transition from stability to complex instability: an analytical approach using 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 a Hamiltonian of three degrees of freedom and a family of periodic orbits with a transition from stability to complex instability, such that there is an irrational collision of the Floquet eigenvalues of opposite sign. We analize the local dynamics and the bifurcation phenomena linked to this transition. We study the resulting Hamiltonian Hopf-like bifurcation from an analy- tical point of view by means of normal forms. The existence of a bifurcating family of 2D tori is derived in both cases (direct and inverse bifur- cation) are described.
Hamiltonian dynamical systems
Lagrangian functions
Hamiltonian systems
normal forms
complex instability
bifurcation
Hamilton, Sistemes de
Lagrange, Funcions de
Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
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