Transport of passive scalars in  geophysical flows has been described in recent years in the framework of  the theory of dynamical systems. These flows are mainly aperiodic and therefore 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. 

In this presentation we propose 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 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.