Examinando por Autor "Vallejo, Juan C"

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Characterization of the local instability in the Hénon–Heiles Hamiltonian
(Elsevier, 2003-03-07) Vallejo, Juan C; Aguirre, Jacobo; Sanjuán, Miguel A.F.
Several prototypical distributions of finite-time Lyapunov exponents have been computed for the two-dimensional Hénon– Heiles Hamiltonian system. Different shapes are obtained for each dynamical state. Even when an evolution is observed in the morphology of the distributions for the smallest integration intervals, they can still serve for characterizing the dynamical state of the system.
Dynamical Monte Carlo Simulations of 3-D Galactic Systems in Axisymmetric and Triaxial Potentials
(Cambridge University Press, 2017) Taani, Ali; Vallejo, Juan C
Influence of the gravitational radius on asymptotic behavior of the relativistic Sitnikov problem
(American Physical Society, 2020) Bernal, Juan D.; Seoane, Jesus; Vallejo, Juan C; Huang, Liang; Sanjuán, Miguel A.F.
The Sitnikov problem is a classical problem broadly studied in physics which can represent an illustrative example of chaotic scattering. The relativistic version of this problem can be attacked by using the post- Newtonian formalism. Previous work focused on the role of the gravitational radius λ on the phase space portrait. Here we add two relevant issues on the influence of the gravitational radius in the context of chaotic scattering phenomena. First, we uncover a metamorphosis of the KAM islands for which the escape regions change insofar as λ increases. Second, there are two inflection points in the unpredictability of the final state of the system when λ ≃ 0.02 and λ ≃ 0.028. We analyze these inflection points in a quantitative manner by using the basin entropy. This work can be useful for a better understanding of the Sitnikov problem in the context of relativistic chaotic scattering. In addition, the described techniques can be applied to similar real systems, such as binary stellar systems, among others.
Local predictability and nonhyperbolicity through finite Lyapunov exponent distributions in two-degrees-of-freedom Hamiltonian systems
(American Physical Society, 2008) Vallejo, Juan C; Viana, Ricardo L.; Sanjuán, Miguel A.F.
By using finite Lyapunov exponent distributions, we get insight into both the local and global properties of a dynamical flow, including its nonhyperbolic behavior. Several distributions of finite Lyapunov exponents have been computed in two prototypical four-dimensional phase-space Hamiltonian systems. They have been computed calculating the growth rates of a set of orthogonal axes arbitrarily pointed at given intervals. We analyze how such distributions serve or not for tracing the orbit nature and local flow properties such as the unstable dimension variability, as the axes are allowed or not to tend to the largest stretching direction. The relationship between the largest and closest to zero exponent distribution is analyzed. It shows a linear depen- dency at short intervals, related to the number of degrees of freedom of the system. Finally, the hyperbolicity indexes, associated to the shadowing times, are calculated. They provide interesting information at very local scales, even when there are no Gaussian distributions and the values cannot be regarded as random variables.