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Distinguished trajectories in time dependent vector fields
We introduce a new definition of distinguished trajectory that generalises
the concepts of fixed point and periodic orbit to aperiodic dynamical systems.
This new definition is valid for identifying distinguished trajectories with
hyperbolic and non-hyperbolic types of stability. The definition is implemented
numerically and the procedure consist in 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 characterises distinguished trajectories in finite time
intervals, and states that outside these intervals trajectories are no longer
distinguished.Comment: Chaos 19 (2009), 013111-1-013111-1