Numerical analysis of transport in dynamical systems

Abstract

Transport processes play an important role in many natural phenomena. Prominent examples are the chaotic advection of fluid particles in geophysical flows or the transport of asteroids and comets in the solar system. Similar transport mechanisms are also at work in chemical physics explaining for example the transition between different conformations of molecules or the kinematics of chemical reactions. Therefore, in the numerical analysis of such dynamical systems one is interested in the identification of those regions in phase space that are involved in the transport process. In this context, invariant manifolds of hyperbolic objects play a crucial role as these structures are known to form natural barriers to transport ...