Brian Arthur Coomes

Assoc. Professor

Phone:
(305) 284-6987
Locator Code:
4250
 
About

Current Research

Chaotic dynamical systems provide a rich source of fascinating examples for the mathematical community. However, much of what is believed to be true about such systems has not been rigorously verified, only inferred from numerical experimentation. My work, largely joint with Hüseyin Koçak and Kenneth J. Palmer, bridges the gap between numerical experimentation and rigorous mathematical analysis by a technique called shadowing. Using this technique we have been successful in computing uniform estimates of solutions of chaotic dynamical systems over long time intervals and we have been able to prove the existence and accurately describe periodic orbits of dynamical systems, some with surprisingly long periods. We have now turned our attention to obtaining new classes of results via shadowing.

Career

Education

1988Ph.D. University of Nebraska at Lincoln

LIST OF SPECIALTIES: Differential Equations, Dynamical Systems

Research

LIST OF SPECIALTIES: Differential Equations, Dynamical Systems

Publications

Brian Coomes, Hüseyin Koçak and Kenneth J. Palmer "Transversal Connecting Orbits from Shadowing" Numerische Mathematik 427--469106 (2007).


Brian Coomes, Hüseyin Koçak and Kenneth J. Palmer "Shadowing in ODE's" Rendiconti del Seminario Matematico 89--11465 (2007).


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