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, 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.
Vladimir Igorevich Arnold was a Soviet and Russian mathematician. While he is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, he made important contributions in several areas including dynamical systems theory, algebra, catastrophe theory, topology, algebraic geometry, symplectic geometry, differential equations, classical mechanics, hydrodynamics and singularity theory, including posing the ADE classification problem, since his first main result—the solution of Hilbert's thirteenth problem in 1957 at the age of 19. He co-founded two new branches of mathematics—KAM theory, and topological Galois theory.
Oscar Zariski was a Russian-born American mathematician and one of the most influential algebraic geometers of the 20th century.
In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it on the floor, and flattening it. In some places the flat string will cross itself in an approximate "X" shape. The points on the floor where it does this are one kind of singularity, the double point: one bit of the floor corresponds to more than one bit of string. Perhaps the string will also touch itself without crossing, like an underlined "U". This is another kind of singularity. Unlike the double point, it is not stable, in the sense that a small push will lift the bottom of the "U" away from the "underline".
Sergei Petrovich Novikov is a Soviet and Russian mathematician, noted for work in both algebraic topology and soliton theory. In 1970, he won the Fields Medal.
Igor Rostislavovich Shafarevich was a Soviet and Russian mathematician who contributed to algebraic number theory and algebraic geometry. Outside mathematics, he wrote books and articles that criticised socialism and other books which were (controversially) described as anti-semitic.
The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories.
John Norman Mather was a mathematician at Princeton University known for his work on singularity theory and Hamiltonian dynamics. He was descended from Atherton Mather (1663–1734), a cousin of Cotton Mather. His early work dealt with the stability of smooth mappings between smooth manifolds of dimensions n and p. He determined the precise dimensions (n,p) for which smooth mappings are stable with respect to smooth equivalence by diffeomorphisms of the source and target.
In the mathematical theory of knots, a finite type invariant, or Vassiliev invariant, is a knot invariant that can be extended to an invariant of certain singular knots that vanishes on singular knots with m + 1 singularities and does not vanish on some singular knot with 'm' singularities. It is then said to be of type or order m.
Peter John Giblin is an English mathematician whose primary research involves singularity theory and its application to geometry, computer vision, and computer graphics. Giblin is an emeritus professor of mathematics at the University of Liverpool where he has served on staff for more than 40 years. His positions at Liverpool have included Head of Department, and Head of Division.
Victor Anatolyevich Vassiliev or Vasilyev, is a Soviet and Russian mathematician. He is best known for his discovery of the Vassiliev invariants in knot theory, which subsume many previously discovered polynomial knot invariants such as the Jones polynomial. He also works on singularity theory, topology, computational complexity theory, integral geometry, symplectic geometry, partial differential equations, complex analysis, combinatorics, and Picard–Lefschetz theory.
Anatoly Aleksandrovich Zhigljavsky is a professor of Statistics in the School of Mathematics at Cardiff University. He has authored 12 monographs and over 150 papers in refereed journals. His research interests include stochastic and high-dimensional global optimisation, time series analysis, multivariate data analysis, statistical modeling in market research, probabilistic methods in search and number theory.
Ian Robertson Porteous was a Scottish mathematician at the University of Liverpool and an educator on Merseyside. He is best known for three books on geometry and modern algebra. In Liverpool he and Peter Giblin are known for their registered charity Mathematical Education on Merseyside which promotes enthusiasm for mathematics through sponsorship of an annual competition.
Euler calculus is a methodology from applied algebraic topology and integral geometry that integrates constructible functions and more recently definable functions by integrating with respect to the Euler characteristic as a finitely-additive measure. In the presence of a metric, it can be extended to continuous integrands via the Gauss–Bonnet theorem. It was introduced independently by Pierre Schapira and Oleg Viro in 1988, and is useful for enumeration problems in computational geometry and sensor networks.
Victor Ivrii, is a Russian, Canadian mathematician who specializes in analysis, microlocal analysis, spectral theory and partial differential equations. He is a professor at the University of Toronto Department of Mathematics.
Adi Ben-Israel is a mathematician and an engineer, working in applied mathematics, optimization, statistics, operations research and other areas. He is a Professor of Operations Research at Rutgers University, New Jersey.
Alexander Nikolaevich Gorban is a scientist of Russian origin, working in the United Kingdom. He is a professor at the University of Leicester, and director of its Mathematical Modeling Centre. Gorban has contributed to many areas of fundamental and applied science, including statistical physics, non-equilibrium thermodynamics, machine learning and mathematical biology.
Anton V. Zorich is a Russian mathematician at the Institut de mathématiques de Jussieu. He is the son of Vladimir A. Zorich. He received his Ph.D. from Moscow State University under the supervision of Sergei Novikov.
Sabir Medgidovich Gusein-Zade is a Russian mathematician and a specialist in singularity theory and its applications.
Vladimir Mikhailovich Zakalyukin was a Russian mathematician known for his research on singularity theory, differential equations, and optimal control theory.
