In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a set, without the need of a smooth space-time structure defined on it.
David Pierre Ruelle is a Belgian mathematical physicist, naturalized French. He has worked on statistical physics and dynamical systems. With Floris Takens, Ruelle coined the term strange attractor, and developed a new theory of turbulence.
In mathematics, a heteroclinic cycle is an invariant set in the phase space of a dynamical system. It is a topological circle of equilibrium points and connecting heteroclinic connections. If a heteroclinic cycle is asymptotically stable, approaching trajectories spend longer and longer periods of time in a neighbourhood of successive equilibria.
Jerrold Eldon Marsden was a Canadian mathematician. He was the Carl F. Braun Professor of Engineering and Control & Dynamical Systems at the California Institute of Technology. Marsden is listed as an ISI highly cited researcher.
V. Balakrishnan is an Indian theoretical physicist who has worked in a number of fields and areas, including particle physics, many-body theory, the mechanical behavior of solids, dynamical systems, stochastic processes, and quantum dynamics. He is an accomplished researcher who has made important contributions to the theory of anelasticity, continuous-time random walks, and recurrences in dynamical systems.
Albert Joseph Libchaber is a Detlev W. Bronk Professor at The Rockefeller University. He won the Wolf Prize in Physics in 1986. In 1999 he received the Prix des Trois Physiciens from the Fondation de France.
John Mark Guckenheimer joined the Department of Mathematics at Cornell University in 1985. He was previously at the University of California at Santa Cruz (1973-1985). He was a Guggenheim fellow in 1984, and was elected president of the Society for Industrial and Applied Mathematics (SIAM) and served as president 1997–1998. Guckenheimer received his B.A. from Harvard University in 1966 and his Ph.D. from the University of California at Berkeley in 1970. His Ph.D. thesis advisor was Stephen Smale.
A. K. M. Fazle Hussain is a professor of mechanical engineering at Texas Tech University.
Philip Geoffrey Saffman FRS was a mathematician and the Theodore von Kármán Professor of Applied Mathematics and Aeronautics at the California Institute of Technology.
Stephen Ray Wiggins is a Cherokee-American applied mathematician also of British heritage best known for his contributions in nonlinear dynamics, chaos theory and nonlinear phenomena, with applications to Lagrangian aspects of fluid transport and mixing and phase space aspects of theoretical chemistry.
Roger Meyer Temam is a French applied mathematician working in numerical analysis, nonlinear partial differential equations and fluid mechanics. He graduated from the University of Paris – the Sorbonne in 1967, completing a doctorate under the direction of Jacques-Louis Lions. He has published over 400 articles, as well as 12 books.
John Leask Lumley was an American fluid dynamicist and a professor at Cornell University. He is widely known for his research in turbulence and is the coauthor of A First Course in Turbulence along with Hendrik Tennekes.
Florin Nicolae Diacu was a Romanian Canadian mathematician and author.
(John) Trevor Stuart FRS is a mathematician and senior research investigator at Imperial College London working in theoretical fluid mechanics, hydrodynamic stability of fluid flows and nonlinear partial differential equations.
Ahmet Cemal Eringen was a Turkish- American engineering scientist. He was a professor at Princeton University and the founder of the Society of Engineering Science. The Eringen Medal is named in his honor.
Robert W. Ghrist is an American mathematician, known for his work on topological methods in applied mathematics.
Model order reduction (MOR) is a technique for reducing the computational complexity of mathematical models in numerical simulations. As such it is closely related to the concept of metamodeling, with applications in all areas of mathematical modelling.
Mark Iosifovich Freidlin is a Russian-American probability theorist who works as a Distinguished University Professor of Mathematics at the University of Maryland, College Park. He is one of the namesakes of the Freidlin–Wentzell theory, which is an important part of the large deviations theory. Freidlin and Wentzell are the authors of the first monograph on the large deviations theory for stochastic processes (1979). The Freidlin-Wentzell theory describes, in particular, the long-time effects caused by random perturbations. The latest edition of the book was published by Springer in 2012. It contains not just the results on large deviations but also new results on other asymptotic problems, in particular, on the averaging principle for stochastic perturbations. Other works of Mark Freidlin concern perturbations of Hamiltonian systems, wave front propagation in reaction-diffusion equations, non-linear perturbations of partial differential equations. stochasticity in deterministic dynamical systems.
Dwight Barkley is a professor of mathematics at the University of Warwick.
Jack Kenneth Hale was an American mathematician working primarily in the field of dynamical systems and functional differential equations.
