58 citations · 422 across the 35 of their papers we have counts for
35 papers
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…
Conservative quasipolynomial maps
Benito Hernández-Bermejo, Léon Brenig
The existence of conservative quasipolynomial (QP) maps is investigated. A classification is given for dimensions two and three, and the analytical solution of the former case is c…
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…
Heisenberg's principle: a cosmological speculation
Benito Hernández-Bermejo
It is shown how the uncertainty principle can provide a mechanism for the generation of fluctuations of very diverse scales in the early universe. This phenomenon could account for…
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…
Characterization, global analysis and integrability of a family of Poisson structures
Benito Hernández-Bermejo
An n-dimensional solution family of the Jacobi equations is characterized and investigated, including the global determination of its main features: the Casimir invariants, the con…
Transition between extinction and blow-up in a generalized Fisher-KPP model
Benito Hernández-Bermejo, Ariel Sánchez-Valdés
Stationary solutions of the Fisher-KPP equation with general nonlinear diffusion and arbitrary reactional kinetic orders terms are characterized. Such stationary (separatrix-like)…
Analytical Quantile Solution for the S-distribution, Random Number Generation and Statistical Data Modeling
Benito Hernández-Bermejo, Albert Sorribas
The selection of a specific statistical distribution is seldom a simple problem. One strategy consists in testing different distributions (normal, lognormal, Weibull, etc.), and se…
Characterization and solvability of quasipolynomial symplectic mappings
Benito Hernández-Bermejo, Léon Brenig
Quasipolynomial (or QP) mappings constitute a wide generalization of the well-known Lotka-Volterra mappings, of importance in different fields such as population dynamics, Physics,…
Characterization and global analysis of a family of Poisson structures
Benito Hernández-Bermejo
A three-dimensional family of solutions of the Jacobi equations for Poisson systems is characterized. In spite of its general form it is possible the explicit and global determinat…
New four-dimensional solutions of the Jacobi equations for Poisson structures
Benito Hernández-Bermejo
A new four-dimensional family of skew-symmetric solutions of the Jacobi equations for Poisson structures is characterized. As a consequence, previously known types of Poisson struc…
Algebraic decoupling of variables for systems of ODEs of quasipolynomial form
Benito Hernández-Bermejo, Victor Fairén
A generalization of the reduction technique for ODEs recently introduced by Gao and Liu is given. It is shown that the use of algebraic methods allows the extension of the procedur…
Equivalence and finite time blow-up of solutions and interfaces for two nonlinear diffusion equations
Benito Hernández-Bermejo, Razvan Gabriel Iagar, Pilar R. Gordoa +2
In this work, we construct a transformation between the solutions to the following reaction-convection-diffusion equation posed f…
Computing Casimir invariants from Pfaffian systems
T. W. Yudichak, Benito Hernández-Bermejo, P. J. Morrison
We describe a method for computing Casimir invariants that is applicable to both finite and infinite-dimensional Poisson brackets. We apply the method to various finite and infinit…
Simple evaluation of Casimir invariants in finite-dimensional Poisson systems
Benito Hernández-Bermejo, V. Fairén
In this letter we present a procedure for the calculation of the Casimir functions of finite-dimensional Poisson systems which avoids the burden of solving a set of partial differe…
A constant of motion in 3D implies a local generalized Hamiltonian structure
Benito Hernández-Bermejo, Victor Fairén
We demonstrate that a Poisson structure can always be associated to a general nonautonomous 3D vector field of ODEs by means of a diffeomorphism that preserves both the orientation…
New solutions of the Jacobi equations for three-dimensional Poisson structures
Benito Hernández-Bermejo
A systematic investigation of the skew-symmetric solutions of the three-dimensional Jacobi equations is presented. As a result, three disjoint and complementary new families of sol…
One solution of the 3D Jacobi identities allows determining an infinity of them
Benito Hernández-Bermejo
It is demonstrated that the knowledge of a single and arbitrary solution of the three-dimension\-al Jacobi equations allows determining infinite families of new solutions, which ar…
Local Stability and Lyapunov Functionals for n-Dimensional Quasipolynomial Conservative Systems
Benito Hernández-Bermejo, Victor Fairén
We present a method for determining the local stability of equilibrium points of conservative generalizations of the Lotka-Volterra equations. These generalizations incorporate bot…
Algebraic recasting of nonlinear systems of ODEs into universal formats
Benito Hernández-Bermejo, Victor Fairén, Léon Brenig
It is sometimes desirable to produce for a nonlinear system of ODEs a new representation of simpler structural form, but it is well known that this goal may imply an increase in th…
Hamiltonian structure and Darboux theorem for families of generalized Lotka-Volterra systems
Benito Hernández-Bermejo, Victor Fairén
This work is devoted to the establishment of a Poisson structure for a format of equations known as Generalized Lotka-Volterra systems. These equations, which include the classical…