Felipe Garcia Ramos Aguilar
Mathematics, UBC

Tue 31 Mar 2015, 12:30pm
SPECIAL
One Time Event
Room 203 of the Graduate Student Centre (6371 Crescent Road), UBC

Doctoral Exam: Randomness and Structure in Dynamical Systems: Different Forms of Sensitivity and Equicontinuity

Room 203 of the Graduate Student Centre (6371 Crescent Road), UBC
Tue 31 Mar 2015, 12:30pm2:30pm
Details
In this thesis we study topological (continuous map on a compact metric space) and measure theoretical (measure preserving map on a probability space) dynamical systems.
Dynamical systems range from chaotic (random) to predictable (high structure). Structure and randomness can be represented with different forms of equicontinuity and sensitivity to initial conditions (sensitivity).
Inspired by the classical dichotomy between sensitivity and equicontinuity we define weak forms of topological and measure theoretical equicontinuity and strong forms of sensitivity for dynamical systems, and we study their relationships with spectral properties and sequence entropy. We also prove results of how measure theoretically equicontinuous cellular automata (a particular class of topological systems with close connections to computer science) behave in the long term.
The work of this thesis answers questions from  B. Scarpellini. Stability properties of flows with pure point spectrum. Journal of the London Mathematical Society, 2(3):451–464, 1982.  F. Blanchard and P. Tisseur. Some properties of cellular automata with equicontinuity points. Annales de l’Institut Henri Poincare (B) Probability and Statistics, 36(5):569 – 582, 2000.
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Mon 25 May 2015, 11:30am
SPECIAL
One Time Event
MATH 126

Mathematics Grad Reception

MATH 126
Mon 25 May 2015, 11:30am1:00pm
Details
The luncheon and awards presentation will be followed by the Niven Lecture at 1:15pm.
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