58 citations · 418 across the 34 of their papers we have counts for
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Perturbed rank 2 Poisson systems and periodic orbits on Casimir invariant manifolds
Isaac A. García, Benito Hernández-Bermejo
A class of n-dimensional Poisson systems reducible to an unperturbed harmonic oscillator shall be considered. In such case, perturbations leaving invariant a given symplectic leaf…
Inverse Jacobi multiplier as a link between conservative systems and Poisson structures
Isaac A. García, Benito Hernández-Bermejo
Some aspects of the relationship between conservativeness of a dynamical system (namely the preservation of a finite measure) and the existence of a Poisson structure for that syst…
Periodic orbits in analytically perturbed Poisson systems
Isaac A. García, Benito Hernández-Bermejo
Analytical perturbations of a family of finite-dimensional Poisson systems are considered. It is shown that the family is analytically orbitally conjugate in $U \subset \mathbb{R}^…
Poisson systems as the natural framework for additional first integrals via Darboux invariant hypersurfaces
Isaac A. García, Benito Hernández-Bermejo
In the literature, the existence of Darboux polynomials and additional polynomial first integrals has been considered in the case of Hamiltonian systems. In this article such probl…
Perturbed Euler top and bifurcation of limit cycles on invariant Casimir surfaces
Isaac A. García, Benito Hernández-Bermejo
Analytical perturbations of the Euler top are considered. The perturbations are based on the Poisson structure for such a dynamical system, in such a way that the Casimir invariant…
New solution family of the Jacobi equations: Characterization, invariants, and global Darboux analysis
Benito Hernández-Bermejo
A new family of skew-symmetric solutions of the Jacobi partial differential equations for finite-dimensional Poisson systems is characterized and analyzed. Such family has some rem…