Aperiodic geophysical flows are  poorly understood as theory which

is well established in autonomous or periodic flows is not directly applicable to them.  In stationary flows the idea of  fixed point is a keystone to describe geometrically the solutions of the dynamical system.  The concept of fixed point is extended to time periodic flows by means of the Poincaré map, as periodic orbits with T period become fixed points on the Poincaré map.

To gain insight on the geometrical structure of  aperiodic flows typically 

are used concepts such as Lyapunov exponents  and its  finite time versions (FSLE and FTLE). In this presentation we propose to this end 

a generalisation of the concept of fixed point  to aperiodic dynamical

systems: the distinguished trajectory. In the context of highly aperiodic realistic flows our definition characterizes trajectories  and states that they  hold  the property of being distinguished in a finite time interval.

Previous works by Ide et al. and Ju  et al. have addressed the existence of

distinguished hyperbolic trajectories but our  new definition  shows that 

non-hyperbolic orbits  may also fall within this category. This type of trajectories might be of special interest for their applications in oceanography as they are related  to eddies or vortices.