Vitor Martins de Oliveira

University of São Paulo | USP · Institute of Mathematics and Statistics (IME) (São Paulo)

Hamiltonian systems that are either open, leaking, or contain holes in the phase space possess solutions that eventually escape the system’s domain. The motion described by such escape orbits before crossing the escape threshold can be understood as a transient behavior. In this work, we introduce a numerical method to visually illustrate and quant...

This software was developed to numerically investigate the dynamical and geometrical aspects of the planar circular restricted three-body problem. It is entirely written in c and most of the functions use the Gnu Scientific Library. In order to use it, open the main.c file and uncomment the function you want. You might have to input some values suc...

Invariant manifolds are the skeleton of the chaotic dynamics in Hamiltonian systems. In Celestial Mechanics, for instance, these geometrical structures are applied to a multitude of physical and practical problems, such as to the description of the natural transport of asteroids and to the construction of trajectories for artificial satellites. In...

Invariant manifolds are the skeleton of the chaotic dynamics in Hamiltonian systems. In Celestial Mechanics, for instance, these geometrical structures are applied to a multitude of physical and practical problems, such as to the description of the natural transport of asteroids and to the construction of trajectories for artificial satellites. In...

In this work, we investigate the Earth-Moon system, as modeled by the planar circular restricted three-body problem, and relate its dynamical properties to the underlying structure associated with specific invariant manifolds. We consider a range of Jacobi constant values for which the neck around the Lagrangian point L1 is always open, but the orb...

In this work, we introduce the escape measure, a finite-time version of the natural measure, to investigate the transient dynamics of escape orbits in open Hamiltonian systems. In order to numerically calculate the escape measure, we cover a region of interest of the phase space with a grid and we compute the visitation frequency of a given orbit o...

In this work, we investigate the Earth-Moon system, as modeled by the planar circular restricted three-body problem, and relate its dynamical properties to the underlying structure associated to specific invariant manifolds. We consider a range of Jacobi constant values for which the neck around the Lagrangian point $L_1$ is always open but the orb...

Stickiness is a well known phenomenon in which chaotic orbits expend an expressive amount of time in specific regions of the chaotic sea. This phenomenon becomes important when dealing with area-preserving open systems because, in this case, it leads to a temporary trapping of orbits in certain regions of phase space. In this work, we propose that...

Stickiness is a well known phenomenon in which chaotic orbits expend an expressive amount of time in specific regions of the chaotic sea. This phenomenon becomes important when dealing with area-preserving open systems because, in this case, it leads to a temporary trapping of orbits in certain regions of phase space. In this work, we propose that...

We introduce a map which reproduces qualitatively many fundamental properties of the dynamics of heavy particles in fluid flows. These include a uniform rate of decrease of volume in phase space, a slow-manifold effective dynamics when the single parameter s (analogous of the Stokes number) approaches zero, the possibility of fold caustics in the “...

Precise control and manipulation of individual drops are crucial in many lab-on-a-chip applications. We present a novel hybrid concept for channel-based discrete microfluidics with integrated electrowetting functionality by incorporating co-planar electrodes (separated by a narrow gap) in one of the microchannel walls. By combining the high through...