1 Rev. Inv. Fis. 18. 151802551 (2015) Structure of the Velocity during a Chaotic Episode Javier Montenegro Joo Facultad de Ciencias Físicas, Universidad Nacional Mayor de San Marcos (UNMSM, Lima Perú) VirtualDynamics: Science & Engineering Virtual Labs Director@VirtualDynamics.Org www.VirtualDynamics.Org Abstract An investigation on the structure of the velocity in the nonlinear damped and forced oscillator, during a chaotic episode has been carried out. It has been found that the extreme values of the velocity show a bifurcating cascade as time elapses, just like the cascade detected in the extremes of oscillation amplitudes versus time, which leads to the very well-known bifurcation cascade of the periods during a chaotic event. It has been encountered that displacement and velocity during a chaotic episode in the investigated system, keep both similar configurations. This analogous structure detected in displacement and velocity suggests the possibility that these two magnitudes share the same pattern in other chaotic systems. Keywords: nonlinear oscillations, chaos, displacement, velocity, Poincare Maps. Estructura de la velocidad durante un episodio caótico Resumen Se ha realizado una investigación sobre la estructura de la velocidad en el oscilador no-lineal forzado y amortiguado, durante un episodio caótico. Se ha encontrado que los valores extremos de la velocidad muestran una cascada de bifurcación a medida que transcurre el tiempo, tal como la que se observa en los valores extremos de la amplitud de oscilación versus tiempo, lo cual conduce a la muy bien conocida cascada de bifurcación del periodo de la oscilación durante un episodio caótico. Se ha encontrado que el desplazamiento y la velocidad durante un evento caótico en el sistema investigado, mantienen ambos configuraciones similares. La estructura análoga detectada en el desplazamiento y la velocidad sugiere la posibilidad de que estas dos magnitudes manifiesten el mismo esquema en otros sistemas caóticos. Palabras clave: oscilaciones no-lineales, caos, desplazamiento, velocidad, Mapas de Poincaré. Introduction From elementary oscillations theory, specifically from the simple harmonic motion (SHM), it is known that the velocity and acceleration of an oscillator also oscillate as time elapses. The SHM is a smooth oscillatory motion with smooth velocity and acceleration, where the displacement, the velocity and the acceleration have all the same structure, the three are harmonic functions of time. Obviously it is intuitively expected that a chaotic oscillator must have both, disordered velocity and disordered acceleration, even more, from the experience with the SHM it is expected that displacement, and velocity and acceleration must share the same pattern. When watching with the naked eye and in slow motion [1] the (x,v,t) evolution in State Space, it results evident that the velocity of a chaotic oscillator is rather messy; this may also be appreciated in Figure 1, which shows a fragment of a chaotic event, in