TITLE: Does Differential Topology or Differential Geometry play a larger role in Chaos Theory?
QUESTION [8 upvotes]: I'm an undergraduate on somewhat of a time constraint in school.  I have room in my remaining schedule for a semester of either Differential Geometry or Differential Topology.  
I understand the topological side deals with primarily global aspects of a manifold, whereas the geometrical side associates with interesting local structures.  
To be concise-  I'm interested in chaotic dynamical systems and P.D.E., so which subject would be more worthwhile, i.e. which subject's vocabulary/method would equip for further reading in the topics I am interested in?  Or am i naive in forcing myself to choose between the two topics, as similar as they are?
Thank you!

REPLY [2 votes]: I took both. I feel differential geometry is more tangible and computational, while differential topology is more conceptual.