Jacob Palis Jr. is a Brazilian mathematician and professor. Palis' research interests are mainly dynamical systems and differential equations. Some themes are global stability and hyperbolicity, bifurcations, attractors and chaotic systems.
Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values of a system causes a sudden 'qualitative' or topological change in its behavior. Bifurcations occur in both continuous systems and discrete systems. The name "bifurcation" was first introduced by Henri Poincaré in 1885 in the first paper in mathematics showing such a behavior. Henri Poincaré also later named various types of stationary points and classified them with motif.
Demetrios Christodoulou is a Greek mathematician and physicist, who first became well known for his proof, together with Sergiu Klainerman, of the nonlinear stability of the Minkowski spacetime of special relativity in the framework of general relativity. Christodoulou is a 1993 MacArthur Fellow.
In the mathematical theory of bifurcations, a Hopfbifurcation is a critical point where a system's stability switches and a periodic solution arises. More accurately, it is a local bifurcation in which a fixed point of a dynamical system loses stability, as a pair of complex conjugate eigenvalues—of the linearization around the fixed point—crosses the complex plane imaginary axis. Under reasonably generic assumptions about the dynamical system, a small-amplitude limit cycle branches from the fixed point.
Reaction–diffusion systems are mathematical models which correspond to several physical phenomena. The most common is the change in space and time of the concentration of one or more chemical substances: local chemical reactions in which the substances are transformed into each other, and diffusion which causes the substances to spread out over a surface in space.
Paul Glendinning is a Professor of Applied Mathematics, in the School of Mathematics at the University of Manchester who is known for his work on dynamical systems, specifically models of the time-evolution of complex mathematical or physical processes. His main areas of research are bifurcation theory ; synchronization and blowout bifurcations; low-dimensional maps; and quasi-periodically forced systems.
Stephen Ray Wiggins is an American, British and Cherokee applied mathematician 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.
Valentin Afraimovich was a Soviet, Russian and Mexican mathematician. He made contributions to dynamical systems theory, qualitative theory of ordinary differential equations, bifurcation theory, concept of attractor, strange attractors, space-time chaos, mathematical models of nonequilibrium media and biological systems, traveling waves in lattices, complexity of orbits and dimension-like characteristics in dynamical systems.
In mathematics, a periodic travelling wave is a periodic function of one-dimensional space that moves with constant speed. Consequently, it is a special type of spatiotemporal oscillation that is a periodic function of both space and time.
Jack Kenneth Hale was an American mathematician working primarily in the field of dynamical systems and functional differential equations.
Frank Merle is a French mathematician, specializing in partial differential equations and mathematical physics.
Albert Baernstein II was an American mathematician.
George Roger Sell was an American mathematician, specializing in differential equations, dynamical systems, and applications to fluid dynamics, climate modeling, control systems, and other subjects.
Pierre Collet is a French mathematical physicist, specializing in statistical mechanics, stochastic processes, and chaos theory.
Zhihong "Jeff" Xia is a Chinese-American mathematician.
Edward Norman Dancer FAA is an Australian mathematician, specializing in nonlinear analysis.
Geneviève Raugel was a French mathematician working in the field of numerical analysis and dynamical systems.
Gustavo A. Ponce is a Venezuelan mathematician.
Gérard Iooss is a French mathematician, specializing in dynamical systems and mathematical problems of hydrodynamics.
Anders Szepessy is a Swedish mathematician.
