D. Phil. (Doctorate), University of Oxford, 2002
Dr. Raines received his doctorate in mathematics from Oxford University where he was a member of St. Edmund's Hall. He travels extensively to work with collaborators in the UK, Italy, Croatia, and New Zealand. He was born and raised in Texas. He is married with three children and loves to go camping and to go running.
Academic Interests and Research:
Dr. Raines research is in the topology of pathological spaces that arise in dynamical systems. He is also interested in applications of topology to non-deterministic dynamical systems that arise in mathematical economics.
"A compact metric space that is universal for orbit spectra of homeomorphisms," joint with C. Good, S. Greenwood and C. Sherman, Advances in Mathematics (2012) no. 5, 2670--2685.
"Fixed points imply chaos for a class of differential inclusions that arise in economic models," joint with D. Stockman, Transactions of the AMS 364 (2012), no. 5, 2479–2492.
"Basins of measures on inverse limit spaces for the induced homeomorphism," joint with J. Kennedy and D. Stockman, Ergodic Theory and Dynamical Systems 30 (2010) 1119--1130.
"A Characterization of Omega-limit sets in shift spaces," joint with A. Barwell, C. Good and R.W. Knight, Ergodic Theory and Dynamical Systems 30 (2010), 21--31.
"A Classification of inverse limit spaces of tent maps with a non-recurrent critical point," joint with S. Stimac, Algebraic and Geometric Topology (2009), 1--34.
NSF Grant DMS 1564721: "50th Spring Topology and Dynamical Systems Conference"
NSF Grant DMS 0604958: "Classifying a model for the Henon Attractor: a U.S. - Croatia Collaboration"
Former Ph.D. Students:
Courses taught at Baylor: