5 papers
On Gauge Poisson Brackets with Prescribed Symmetry
M. Avendaño-Camacho, J. C. Ruíz-Pantaleón, Yu. Vorobiev
In the context of averaging method, we describe a reconstruction of invariant connection-dependent Poisson structures from canonical actions of compact Lie groups on fibered phase…
Geometrical Aspects of the Hamiltonization Problem of Dynamical Systems
Misael Avendaño-Camacho, Claudio C. García-Mendoza, José C. Ruíz-Pantaleón +1
Some positive answers to the problem of endowing a dynamical system with a Hamiltonian formulation are presented within the class of Poisson structures in a geometric framework. We…
Closed stable orbits in a strongly coupled resonant Wilberforce pendulum
Misael Avendaño-Camacho, Alejandra Torres-Manotas, José A Vallejo
We prove the existence of closed stable orbits in a strongly coupled Wilberforce pendulum, for the case of a resonance, by using techniques of geometric singular symplectic r…
A perturbation theory approach to the stability of the Pais-Uhlenbeck oscillator
Misael Avendaño-Camacho, José A. Vallejo, Yury Vorobiev
We present a detailed analysis of the orbital stability of the Pais-Uhlenbeck oscillator, using Lie-Deprit series and Hamiltonian normal form theories. In particular, we explicitly…
Semiclassical Szegö limit of eigenvalue clusters for the hydrogen atom Zeeman Hamiltonian
Misael Avendano-Camacho, Peter D. Hislop, Carlos Villegas-Blas
We prove a limiting eigenvalue distribution theorem (LEDT) for suitably scaled eigenvalue clusters around the discrete negative eigenvalues of the hydrogen atom Hamiltonian formed…