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Theses
Directed
Steven E. Grossman, Ph.D. in Mathematics, 1969 Dissertation: Stability and Asymptotic Behavior of Differential Equations.
Shui-Nee Chow, Ph.D. in Mathematics, 1970 Dissertation: Almost periodic Differential Equation
James Kaplan, Ph.D. in Mathematics, 1970 Dissertation: Some Results in Stability Theory for Ordinary Differential Equations
Stephen H. Saperstone, Ph.D. in Mathematics, 1971 Dissertation: Controllability of Linear Oscillatory Systems Using Positive Controls
Thomas Martin Costello, Ph.D. in Mathematics, 1971 Dissertation: Fundamental Theory of Differential and Integral Equations
Dissertation: On the Controllability and Observability of finite Dimensional Systems
Gina Bari Kolata, M.S. in Mathematics, 1972 Dissertation: A Mathematical Model of Chemical Relaxation to a Cooperative Biochemical Process
Ana Lajmanovich Gergely, Ph.D. in Mathematics, 1974 Dissertation: Mathematical Models and the Control of Infectious Diseases
Tien-Yien Li, Ph.D. in Mathematics, 1974 Dissertation: Dynamics for xn+1 = F(xn)
Glenn Kelly, M.A. in Mathematics, 1974 Dissertation: The Kurzweil-Henstock Integral
Annett Nold, Ph.D. in Mathematics, 1977 Dissertation: Systems Approaching Equilibria in Disease Transmission and Competition for Resources
Ira Schwartz, Ph.D. in Mathematics, 1980 Dissertation: Proving the Existence of Unstable Periodic Orbits Using Computer-Based Estimates
Stephen Pelikan, Ph.D. in
Mathematics from Dissertation: The Dimension of Attractors in Surfaces
Brian Hunt, M.A. in Mathematics, 1983 Dissertation: When All Solutions of x' = ... Oscillate
Tobin Short, M.S. in Applied Mathematics, January 1984 Dissertation: The Development of Chaotic Attractors in the Early Stages of Horseshoe Development
Frank Varosi, M.S. in Applied Mathematics, December 1985 Dissertation: Efficient Use of Disk Storage for Computing Fractal Dimensions
Eric Kostelich, Ph.D. in Applied Mathematics, December 1985 Dissertation: Basin Boundary Structure and Lorenz Cross Sections of the Attractors of the Double Rotor Map
Laura Tedeschini, Ph.D. in Applied Mathematics, June 1986 Dissertation: How Often Do Simple Dynamical Processes Have Infinitely Many Coexisting Sinks?
Peter Battelino, Ph.D. in Physics (co-advisors: Ott, Grebogi), 1987 Dissertation: Three-Frequency Periodicity, Torus Break-up, and Multiple Coexisting Attractors in a Higher Dimensional Dissipative Dynamical System
Zhi-Ping You, Ph.D. in Mathematics, l991 Dissertation: Numerical Study of Stable and Unstable Manifolds of Some Dynamical Systems.
Ying-Cheng Lai, Ph.D. in Physics (co-advisors: Ott, Grebogi), l992 Dissertation: Nonhyperbolicity in Classical and Quantum Chaos.
Troy Shinbrot, Ph.D. in Physics (co-advisors: Hunt, Ott), l992 Dissertation: Controlling Chaos: Using the Butterfly Effect to Direct Trajectories to Targets in Chaotic Systems.
Ivonne Diaz-Rivera, M. A. in Applied Mathematics, 1995 Scholarly Paper: Strange Attractor Reconstruction from Experimental Data: A Review Wai Chin, Ph.D. in Math (co-advisors: Hunt, Ott), 1995 Dissertation: Chaotic Dynamics in Piecewise Smooth Systems. In 2006 Associate Director for Biostatistics at Genzyme
Barry Peratt, Ph.D. in Math at
Dissertation: Mixing Powders and Scrambling Points.
Jacob Miller, Ph.D. in Math at
Dissertation: Finding Periodic Orbits of Maps: Basins of Attraction of Numerical Techniques.
Leon Poon, Ph.D. in Physics (co-advisors: Ott, Grebogi), 1996 Dissertation:
Shadowability, Complexity, and
Ali Fouladi, Ph.D. in Physics (co-advisor: Ott), 1996 Dissertation: Spatio-temperal Patterns and Chaos Control
Ernest Barreto, Ph.D. in Physics (co-advisor: Ott), 1996 Dissertation: Stability in Chaotic Systems
Guo-Hui Yuan, Ph.D. in Physics (co-advisors: Ott, Hunt), 1997 Dissertation: Shipboard Crane Control, Simulated Data Generation and Border - Collision Bifurcations
Guocheng Yuan, Ph.D. in Mathematics (co-advisors: Ott, Hunt), 1999 Dissertation: Properties of Numerical Experiments in Chaotic Dynamical Systems
Carl Robert, Ph.D. in Physics (co-advisors: Ott, Grebogi), 1999 Dissertation: Explosions in Chaotic Dynamical Systems: How New Recurrent Sets Suddenly Appear and a Study of their Periodicities
Josh Tempkin, Ph.D. in Mathematics, 1999 Dissertation: Spurious Lyapunov Exponents Computed Using the Eckmann – Ruelle Procedure
Mitrajit Dutta, Ph.D. in Physics (co-advisor: Ott), 2000 Dissertation: Chaotic Systems Predictable Unpredictabilities and Synchronization
David Sweet, Ph.D. in Physics (co-advisor: Ott), 2000 Dissertation: Higher Dimensional Non Linear Dynamical Systems: Bursting and Scattering
Dhanurjay (DJ) A.S. Patil, Ph.D. in Applied Mathematics, (co-advisors: Ott, Hunt, Kalnay) 2001 Dissertation: Applications of Chaotic Dynamics to Weather Forecasting
Linda J. Moniz, Ph.D. in Mathematics, 2001 Dissertation: Convergence of Dynamically Defined Upper Bounds Sets
Aleksey Zimin,
Ph.D. in Physics, 2003 (co-advisor; Dissertation: The Bubbling Transition and Data Assimilation
Michael Roberts, Ph.D. in Computer Science, 2003 (Samir Khuller was the official CS adviser) Dissertation: A Preprocessor for Shotgun Assembly of Large Genomes
Michael
Oczkowski, Ph.D. in Physics, 2003 (co-advisor with Dissertation: Scenarios for the Development of Locally Low Dimensional Atmospheric Dynamics Kathleen A. Meloney, M.A. in Mathematics, 2004 Thesis: A Dynamical Systems approach to Estimating the Sequences of Repeat Regions in the Genome William Ott, Ph.D. in Mathematics, 2004 (co-advisors: B. Hunt & D. Levermore) Dissertation: Infinite-Dimensional Dynamical Systems and Projections Brandy L. Rapatski, Ph.D. in Applied Mathematics and Scientific Computation, 2004 (co-advisor: F. Suppe) Dissertation: The Non-Linear Transmission Dynamics of HIV/AIDS Cevat Ustun, Ph.D. in Physics, 2005 (co-advisor: B. Hunt) Dissertation: Improving Genome Assembly Ian Frommer, Ph.D. in Applied Math and Sci. Computing, 2005 (co-advisors: Hunt & Bruce Golden) Dissertation: Modeling and Optimization of Transmission Networks Ryan Lance, Ph.D. in Mathematics, 2005 (co-advisor: B. Hunt) Dissertation: Joseph Skufca, Ph.D. in Mathematics, 2005 Dissertation: Understanding a Chaotic Saddle with Focus On A 9-Variable Model of Planar Couette Flow Christopher M. Danforth, Ph.D. in Applied Mathematics, 2006 (co-advisor: E. Kalnay) Dissertation: Making Forecasts for Chaotic Processes in the Presence of Model Error Suzanne S. Sindi, Ph.D. in Applied Mathematics, 2006 (co-advisor: B. Hunt) Dissertation: Describing and Modeling Repeated Sequences in DNA The nonlinear dynamics group generally has students work with several faculty members and as a result students have multiple advisors.
Postdocs
supervised (jointly with collaborators)
Celso Grebogi S. W. McDonald Eric Kostelich Brian Hunt Silvina P. Dawson Ernest Barreto Myong-Hee Sung Lyman Hurd D.J. Patil Crystal Cooper Wayne Hayes, 11/2002 - 6/2004 Aleksey Zimin Michael Roberts Nandi Leslie
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James A. Yorke
Distinguished University Professor of Mathematics and Physics
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A.B., James Yorke came to the He believes a Ph.D. in mathematics is a
license to investigate the universe. His current
research projects range from chaos theory and weather prediction and
genome research and the investigation of computer networks to the population
dynamics of the HIV/AIDS epidemic. He acknowledges the benefits of having superb collaborators! He is perhaps best known to the general
public for coining the mathematical term "chaos" with T.Y. Li in a
1975 paper entitled "Period
Three Implies Chaos". "Chaos" is a mathematical concept
for processes that vary according to precise deterministic laws but appear to
behave in random fashion. The University's
chaos research group, is one of the best in the world. Yorke aims at
describing those robust properties that are common in the dynamics of
physical, biological, and chemical systems. Sometimes he describes the
phenomena using rigorous mathematics, and sometimes only via phenomenological
descriptions from intensive numerical studies. Most often, the research is a
blend of numerical and rigorous techniques. Professor Yorke has coauthored three books
on chaos and a monograph on gonorrhea epidemiology: · Dynamics: Numerical Explorations (written with Helena Nusse) on computational aspects of chaos· Coping with Chaos (written with Edward Ott and Tim Sauer) is a collection of reprints focusing on how scientists observe, quantify, and control chaos.·
Chaos:
An Introduction to Dynamical Systems (written with Kathleen Alligood
and Tim Sauer) -- an interdisciplinary math text for seniors and beginning
graduate students.
Prof.
Yorke has supervised approximately 40 Ph.D.
dissertations in the Depts. of Mathematics, Physics, and Computer
Science. Dr. Yorke's Curriculum Vitae includes a list
of over 300 publications, many with abstracts, and is available online, as is
a short list of those most frequently cited. See also
an
interview on “The Connection” a PBS radio show, an interview
by Tim Sauer on the Dynamical Systems Web Portal, Math 410,
Advanced Calculus, Spring 2006. HIV testing
– the controversy (new 9/2006) Contact Information:
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