To what degree does earning a pure math PhD in dynamical systems limit my career options outside of academia I am a 2nd year math PhD student. If one specializes in pure math (say dynamical systems with no particular real-world application in mind), how difficult can it be to transition into industry after the PhD? What are measures one can take to make this a smooth transition? I am not particularly interested in applied math at the moment, but I'm not too optimistic about the future of the pure mathematician (unless he/she solves some Millennium Prize Problem!!). I would like to think that I have the option of switching from academia to industry if I had to. I am haunted by words of one of my undergrad math professors: "No one should major in pure math. You major in applied math and you continue to study pure math if you're interested in it."

I have a M.A. in math, and my thesis was concerned with estimating the fractal dimension of sets arising in dynamical systems. My ideal profession with a PhD in math would be to teach and to do research. My research need not be limited to pure math.
A lot of PhDs in theoretical mathematics end up "in industry" of one part or another.  Many times this is not by choice, which is sad, but it also means the learning curve is not too steep.  There is a reputation, reasonably well-deserved, that a PhD in mathematics teaches you how to think and solve problems in a rather fundamental and robust way, and that all other skills can be overlaid on top of that.  Certainly I've seen PhDs in "purely theoretical" mathematics with no programming skills, actuarial or statistical knowledge, etc. be hired by industry.  In fact many of these people get on-the-job training in the first year of their job...while they are getting well paid.

Well, but the job market is pretty tight all around these days, as perhaps you've heard.  If being totally clueless outside of theoretical mathematics can land you an industrial job, being less than totally clueless will be even better. I advise PhD students that as soon as they have real thought of a non-academic post-PhD career they should explore this in a positive way, including mentioning it to their advisor so that aspects of their program of study can be adjusted. For instance, in my PhD program you need to take two exams in foreign languages, but one of these can be replaced by a computer project.  Although I think the computer requirement would serve many would-be academics better as well, if you think you may go into industry, then reading in a third language is obviously not going to be as marketable as computer skills.

While you're in a PhD program in mathematics, talk to the students and faculty who have connections and experience in industry.  (Realize that your thesis advisor may not be such a person.  For instance I have zero industrial experience. I do not pretend to give advice in this area -- well, not specific advice, anyway! -- but I try to find other people who can.)  Don't be shy or embarrassed about this.  It's your life and you get to do what you want to do.  

My feeling is that solidifying basic industrially applicable skills -- e.g. programming and even lower-level tech-savviness like spreadsheets, learning how to share and transfer files, etc. -- and supplementing with coursework and other training (e.g. taking actuarial exams; taking one solid course in statistics or financial mathematics) is a better bet and easier to do in your spare time than trying to change your thesis topic to something more applied.  As above, my feeling is that most industrial jobs don't care what you did your thesis on, and having done it on something rarefied and inapplicable is actually fine with them as long as you have, or can make them confident that you can learn, the skills you will need on the job.  But again, talk to people other than the academic lifers like me!