Valentin Afraimovich (, 2 April 1945 – 21 February 2018) was a

Russian Russian(s) may refer to: *Russians (), an ethnic group of the East Slavic peoples, primarily living in Russia and neighboring countries *A citizen of Russia *Russian language, the most widely spoken of the Slavic languages *''The Russians'', a b ...

- Mexican

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

. He made contributions to

dynamical systems theory Dynamical systems theory is an area of mathematics used to describe the behavior of complex systems, complex dynamical systems, usually by employing differential equations by nature of the ergodic theory, ergodicity of dynamic systems. When differ ...

, qualitative theory of

ordinary differential equations In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with any other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives ...

bifurcation theory Bifurcation theory is the Mathematics, mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential e ...

, concept of

attractor In the mathematical field of dynamical systems, an attractor is a set of states toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain c ...

strange attractors In the mathematics, mathematical field of dynamical systems, an attractor is a set of states toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor va ...

space-time In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three-dimensional space, three dimensions of space and the one dimension of time into a single four-dimensional continuum (measurement), continu ...

chaos Chaos or CHAOS may refer to: Science, technology, and astronomy * '' Chaos: Making a New Science'', a 1987 book by James Gleick * Chaos (company), a Bulgarian rendering and simulation software company * ''Chaos'' (genus), a genus of amoebae * ...

mathematical models A mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed ''mathematical modeling''. Mathematical models are used in applied mathemati ...

of non-equilibrium media and

biological systems A biological system is a complex Biological network inference, network which connects several biologically relevant entities. Biological organization spans several scales and are determined based different structures depending on what the system is ...

, travelling

wave In physics, mathematics, engineering, and related fields, a wave is a propagating dynamic disturbance (change from List of types of equilibrium, equilibrium) of one or more quantities. ''Periodic waves'' oscillate repeatedly about an equilibrium ...

s in lattices,

complexity Complexity characterizes the behavior of a system or model whose components interact in multiple ways and follow local rules, leading to non-linearity, randomness, collective dynamics, hierarchy, and emergence. The term is generally used to c ...

orbit In celestial mechanics, an orbit (also known as orbital revolution) is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an ...

s and dimension-like characteristics in

dynamical systems In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models ...

Biography

Afraimovich was born on 2 April 1945 in Kirov,

Soviet Union The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...

. He got his PhD (

Kandidat A Candidate of Sciences is a PhD-equivalent academic research degree in all the post-Soviet countries with the exception of Ukraine, and until the 1990s it was also awarded in Central and Eastern European countries. It is officially classified ...

) degree in 1974 at the Nizhny Novgorod State University under the advice of L. P. Shil'nikov. Also in 1990 he received his

Doctor of Science A Doctor of Science (; most commonly abbreviated DSc or ScD) is a science doctorate awarded in a number of countries throughout the world. Africa Algeria and Morocco In Algeria, Morocco, Libya and Tunisia, all universities accredited by the s ...

degree in Mathematics and Physics, at

Saratov State University Saratov Chernyshevsky State University (, СГУ, transcribed as SGU) is a higher education and research institution in Russia. In 2023 it was ranked #1,156 in the world by ''US News & World Report''. Named for Nikolay Chernyshevsky, the univer ...

in Russia. After then, he held several academic positions, including: * 1992-1995 Visiting Principal Research Scientist,

Georgia Institute of Technology The Georgia Institute of Technology (commonly referred to as Georgia Tech, GT, and simply Tech or the Institute) is a public university, public research university and Institute of technology (United States), institute of technology in Atlanta, ...

Atlanta Atlanta ( ) is the List of capitals in the United States, capital and List of municipalities in Georgia (U.S. state), most populous city in the U.S. state of Georgia (U.S. state), Georgia. It is the county seat, seat of Fulton County, Georg ...

* 1995-1996 Visiting Professor,

Northwestern University Northwestern University (NU) is a Private university, private research university in Evanston, Illinois, United States. Established in 1851 to serve the historic Northwest Territory, it is the oldest University charter, chartered university in ...

Evanston, Illinois Evanston is a city in Cook County, Illinois, United States, situated on the North Shore (Chicago), North Shore along Lake Michigan. A suburb of Chicago, Evanston is north of Chicago Loop, downtown Chicago, bordered by Chicago to the south, Skok ...

* 1996-1998 Visiting Professor,

National Tsing Hua University National Tsing Hua University (NTHU) is a public research university in Hsinchu, Taiwan. It was first founded in Beijing. After the Chinese Civil War, president Mei Yiqi and other academics relocated with the retreating Nationalist government to ...

Hsinchu Hsinchu (, ), officially Hsinchu City, is a city located in northwestern Taiwan. It is the most populous city in Taiwan that is not a special municipality, with estimated 450,655 inhabitants. Hsinchu is a coastal city bordering the Taiwan ...

, Taiwan * 1998–present Professor–researcher, IICO,

Universidad Autónoma de San Luis Potosí The Autonomous University of San Luis Potosí (in ) is a public university in Mexico. It is the largest, oldest, and most comprehensive university in the state of San Luis Potosí, as well as one of the most important ones in Mexico. Among other ...

, San Luis Potosí, Mexico Afraimovich's students include Mark Shereshevsky, Nizhny Novgorod 1990; Todd Ray Young, Atlanta, Georgia, 1995; Antonio Morante, San Luis Potosí (SLP) Mexico, 2002; Salomé Murgia, SLP Mexico, 2003; Alberto Cordonet, SLP Mexico, 2002; Francisco Ordaz, SLP Mexico, 2004; Leticia Ramirez, SLP Mexico, 2005; Irma Tristan-Lopez, SLP Mexico, 2010; Rosendo Vazquez-Bañuelos, 2013. He died on 21 February 2018 in

Nizhny Novgorod Nizhny Novgorod ( ; rus, links=no, Нижний Новгород, a=Ru-Nizhny Novgorod.ogg, p=ˈnʲiʐnʲɪj ˈnovɡərət, t=Lower Newtown; colloquially shortened to Nizhny) is a city and the administrative centre of Nizhny Novgorod Oblast an ...

, Russia.

Selected scientific papers

* VS Afraimovich, G Moses, TR Young. Two dimensional heteroclinic attractor in the generalized Lotka-Volterra system. Nonlinearity 29 (2016). 1645–1667. doi:10.1088/0951-7715/29/5/1645. * V. Afraimovich, X. Gong, M. Rabinovich. Sequential memory: Binding dynamics. Chaos, 5(10):103118, 2015. * V. Afraimovich. M. Courbage, L. Glebsky. Directional Complexity and entropy for Lift Mappings. Discrete and Continuous Dynamical Systems. Series B. Mathematical Modelling, Analysis and Computations. Volume 20, Number 10. December 2015. * Valentin S. Afraimovich, Todd R. Young, Mikhail I. Rabinovich. Hierarchical Heteroclinics in Dynamical Model of Cognitive Processes: Chunking. International Journal of Bifurcation and Chaos Vol. 24, No. 10, 1450132 (2014) * V. S. Afraimovich, L. P. Shilnikov. Symbolic Dynamics in Multidimensional Annulus and Chimera States. International Journal of Bifurcation and Chaos. Vol: 24, N: 08 (August 2014) DOI: 10.1142/S0218127414400021, 1440002 * V. S. Afraimovich, T. Young, M.K. Muezzinglu, M. Rabinovich. Nonlinear Dynamics of Emotion-Cognition Interaction: When Emotion Does Not Destroy Cognition? Bull Math Biol (2011) 73:266-284. DOI 10.1007/s11538-010-9572-x * V. S. Afraimovich, L.A. Bunimovich, S.V. Moreno, Dynamical Networks: Continuous Time and General Discrete Time Models, Regular and Chaotic Dynamics, Vol. 15, 129–147, 2010. * V. Afraimovich, L. Glebsky, Measures Related To ''e,n''-Complexity Functions, Discrete And Continuous Dynamical Systems, Vol. 22, N 12. 2008. * V. S. Afraimovich, M. Rabinovich, R. Huerta, P. Varona, Transient Cognitive Dynamics, Metastability, and Decision Making, PLOS Computational Biology 04, 05: 1–9. 2008. * V. Afraimovich. Some topological properties of lattice dynamical systems, in Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems, eds. J.-R. Chazottes and B. Fernandez, Lecture Notes in Physics, Springer 2005, p 153–180. * V. Afraimovich, V. Zhigulin and M. Rabinovich, On the origin of reproducible sequential activity in neural circuits, Chaos 14 (2004), 1123–1129. * V. Afraimovich, L. Bunimovich and J. Hale, Sistemi dinamici, Storia della Scienza IX, Enciclopedia Italiana 841–850. (2003) * V. Afraimovich, G.M. Zaslavsky, Space time complexity in Hamiltonian dynamics, Chaos, 13, 2, (2003), pp. 519–532. * V. Afraimovich, J. R. Chazottes and A. Cordonet, Synchronization in directionally coupled systems, Discrete Contin. Dyn. Syst., Ser. B, vol. 1 (2001), 421–442. * V. Afraimovich, J.-R. Chazottes and B. Saussol, Local dimensions for Poincare recurrences, Electron.Res.Announc.Amer.Math.Soc., vol.6 (2000), 64–74 * V. Afraimovich and T. Young, Relative density of irrational rotation numbers in families of circle diffeomorphisms. Ergodic theory and dynamical systems, 18 (1998), 1–16. * V. Afraimovich and S-N. Chow, Topological spatial chaos and homoclinic points of Z-d actions in lattice dynamical systems, Japan J. Indust.Appl. Math. 12 1995, 1–17. * V. Afraimovich, S.-N. Chow and W. Liu, Lorenz type attractors from codimensional-one bifurcation, Journal of Dynamics and Differential Equations, 7 (2), 1995, 375–407. * V. Afraimovich and V.I. Nekorkin, Chaos of traveling waves in a discrete chain of di usively coupled maps, International Journal of Bifurcation and Chaos, 4 (3) (1994). * V. Afraimovich and Ya. Pesin, Hyperbolicity of infinite-dimensional drift systems, Nonlinearity, 3 (1990), 1–19. * V. Afraimovich, N.N. Verichev and M.I. Rabinovich, Stochastic synchronization of oscillations in dissipative systems, Radio zika, 29 (9), 1050–1060 (1986) (in Russian). * V. Afraimovich, V.V. Bykov and L.P. Shil'nikov, On attracting nonstructurally stable limiting sets of the type of Lorenz attractor, Trans. of Moscow Math. Soc., 44 (1982). * V. Afraimovich and L.P. Shil'nikov, On critical sets of Morse–Smale systems, Trans. Moscow Math. Soc., 28 (1973).

Selected bibliography

* * * * * * * * * * * * *

Afraimovich award

Afraimovich Award has been granted to outstanding young scholars in nonlinear physical science by NSC since 2020.

References

External links

Personal website

Conference celebrating Afraimovich's 65th anniversary
*
American Institute of Mathematical Sciences

A super short curriculum vitae
*
Torus breakdown article at Scholarpedia

Lagrange Award 2012

Book dedicated to V. Afraimovich

preface
{{DEFAULTSORT:Afraimovich, Valentin 1945 births 2018 deaths 20th-century Russian mathematicians 21st-century Russian mathematicians Soviet mathematicians Mathematical analysts Academic staff of Moscow State University People from Kirov, Kirov Oblast