Distinguished trajectories in time dependent vector fields
Madrid, J. A. Jimenez
Mancho, Ana M.
- Publisher: American Institute of Physics
Nonlinear Sciences - Chaotic Dynamics | Mathematics - Dynamical Systems
We introduce a new definition of distinguished trajectory that generalizes the concepts of fixed point and periodic orbit to aperiodic dynamical systems. This new definition is valid for identifying distinguished trajectories with hyperbolic and nonhyperbolic types of stability. The definition is implemented numerically and the procedure consists of determining a path of limit coordinates. It has been successfully applied to known examples of distinguished trajectories. In the context of highly aperiodic realistic flows our definition characterizes distinguished trajectories in finite time intervals, and states that outside these intervals trajectories are no longer distinguished.