Distinguished trajectories in time dependent vector fields

Details Distinguished trajectories in time dependent vector fields Distinguished trajectories in time dependent vector fields

2008-06-06

arxiv.org/abs/0806.1155v3

Nonlinear Sciences

Chaotic Dynamics

Chaos 19 (2009), 013111-1-013111-18

Scientific paper

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.

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