In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, 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.
Jean-Pierre Vigier was a French theoretical physicist, known for his work on the foundations of physics, in particular on his stochastic interpretation of quantum physics.
In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first integrals that its motion is confined to a submanifold of much smaller dimensionality than that of its phase space.
Nikolay Nikolayevich Bogolyubov, also transliterated as Bogoliubov and Bogolubov, was a Soviet and Russian mathematician and theoretical physicist known for a significant contribution to quantum field theory, classical and quantum statistical mechanics, and the theory of dynamical systems; he was the recipient of the 1992 Dirac Medal.
Anatoly Mykhailovych Samoilenko was a Ukrainian mathematician, an Academician of the National Academy of Sciences of Ukraine, the Director of the Institute of Mathematics of the National Academy of Sciences of Ukraine.
Viktor Yakovlevich Bunyakovsky was a Russian mathematician, member and later vice president of the Petersburg Academy of Sciences.
Aleksei Vasilyevich Pogorelov, was a Soviet mathematician. Specialist in the field of convex and differential geometry, geometric PDEs and elastic shells theory, the author of the novel school textbook on geometry and university textbooks on analytical geometry, on differential geometry, and on foundations of geometry.
In mathematics, secondary calculus is a proposed expansion of classical differential calculus on manifolds, to the "space" of solutions of a (nonlinear) partial differential equation. It is a sophisticated theory at the level of jet spaces and employing algebraic methods.
Objective-collapse theories, also known as models of spontaneous wave function collapse or dynamical reduction models, are proposed solutions to the measurement problem in quantum mechanics. As with other theories called interpretations of quantum mechanics, they are possible explanations of why and how quantum measurements always give definite outcomes, not a superposition of them as predicted by the Schrödinger equation, and more generally how the classical world emerges from quantum theory. The fundamental idea is that the unitary evolution of the wave function describing the state of a quantum system is approximate. It works well for microscopic systems, but progressively loses its validity when the mass / complexity of the system increases.
Damiano Brigo is a mathematician known for research in mathematical finance, filtering theory, stochastic analysis with differential geometry, probability theory and statistics, authoring more than 130 research publications and three monographs. From 2012 he serves as full professor with a chair in mathematical finance at the Department of Mathematics of Imperial College London, where he headed the Mathematical Finance group in 2012–2019. He is also a well known quantitative finance researcher, manager and advisor in the industry. His research has been cited and published also in mainstream industry publications, including Risk Magazine, where he has been the most cited author in the twenty years 1998–2017. He is often requested as a plenary or invited speaker both at academic and industry international events. Brigo's research has also been used in court as support for legal proceedings.
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.
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 non-equilibrium media and biological systems, travelling waves in lattices, complexity of orbits and dimension-like characteristics in dynamical systems.
Sergio Albeverio is a Swiss mathematician and mathematical physicist working in numerous fields of mathematics and its applications. In particular he is known for his work in probability theory, analysis, mathematical physics, and in the areas algebra, geometry, number theory, as well as in applications, from natural to social-economic sciences.
Institute of Mathematics of the National Academy of Sciences of Ukraine is a government-owned research institute in Ukraine that carries out basic research and trains highly qualified professionals in the field of mathematics. It was founded on 13 February 1934.
Irena Lasiecka is a Polish-American mathematician, a Distinguished University Professor of mathematics and chair of the mathematics department at the University of Memphis. She is also co-editor-in-chief of two academic journals, Applied Mathematics & Optimization and Evolution Equations & Control Theory.
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.
Viorel P. Barbu is a Romanian mathematician, specializing in partial differential equations, control theory, and stochastic differential equations.
Sergei Borisovich Kuksin is a French and Russian mathematician, specializing in partial differential equations (PDEs).
Hans J. van Ommeren Dekker is a Dutch theoretical physicist in the line of Dirk Polder, Ralph Kronig, and Nico van Kampen. His scientific work inter alia involves laser theory, path integrals in curved spaces, nonequilibrium statistical mechanics, dissipation in quantum mechanics, and hydrodynamic turbulence. He is director of the Private Institute for Advanced Study and professor emeritus at the Institute for Theoretical Physics of the University of Amsterdam.
Alexandre Mikhailovich Vinogradov was a Russian and Italian mathematician. He made important contributions to the areas of differential calculus over commutative algebras, the algebraic theory of differential operators, homological algebra, differential geometry and algebraic topology, mechanics and mathematical physics, the geometrical theory of nonlinear partial differential equations and secondary calculus.
