Rifkat Ibragimovich Bogdanov (; June 13, 1950 – November 3, 2013) was a

Soviet 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 ...

and

Russia Russia, or the Russian Federation, is a country spanning Eastern Europe and North Asia. It is the list of countries and dependencies by area, largest country in the world, and extends across Time in Russia, eleven time zones, sharing Borders ...

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 ...

known for contributions to

nonlinear dynamical systems 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 p ...

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 ...

, and

differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

. He was an ethnic

Tatar Tatar may refer to: Peoples * Tatars, an umbrella term for different Turkic ethnic groups bearing the name "Tatar" * Volga Tatars, a people from the Volga-Ural region of western Russia * Crimean Tatars, a people from the Crimea peninsula by the B ...

. In his work on bifurcations of

limit cycles In mathematics, in the study of dynamical systems with two-dimensional phase space, a limit cycle is a closed trajectory in phase space having the property that at least one other trajectory spirals into it either as time approaches infinity o ...

and versal deformations of singular points of

vector fields In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space \mathbb^n. A vector field on a plane can be visualized as a collection of arrows with given magnitudes and direct ...

(1975–76), he described a bifurcation of

co-dimension In mathematics, codimension is a basic geometric idea that applies to subspaces in vector spaces, to submanifolds in manifolds, and suitable subsets of algebraic varieties. For affine and projective algebraic varieties, the codimension equals the ...

2, which has become known in the literature as the Bogdanov–Takens bifurcation. Born in the village of Mamykovo in

Tatarstan Tatarstan, officially the Republic of Tatarstan, sometimes also called Tataria, is a Republics of Russia, republic of Russia located in Eastern Europe. It is a part of the Volga Federal District; and its capital city, capital and largest city i ...

, Bogdanov had a doctorate under the supervision of

Vladimir Arnold Vladimir Igorevich Arnold (or Arnol'd; , ; 12 June 1937 – 3 June 2010) was a Soviet and Russian mathematician. He is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, and contributed to s ...

https://mathgenealogy.org/id.php?id=79232 in physico-mathematical sciences and was a professor in two Russian research organizations: the Skobeltsyn Institute of Nuclear Physics at

Lomonosov Moscow State University Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, and six branches. Al ...

and the Department of Higher Mathematics at MATI — the Tsiolkovskii State Technological University.

Selected publications

* R. I. Bogdanov (1975). "Versal deformation of a singular point of a vector field with zero eigenvalues," ''Functional Analysis and Its Applications'' 9: 63

n Russian N, or n, is the fourteenth letter of the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages, and others worldwide. Its name in English is ''en'' (pronounced ), plural ''ens''. History ...

* R. I. Bogdanov (1976). "Bifurcations of the limit cycle of a family of vector fields on a plane," ''Transactions I. G. Petrovskii Seminar, Moscow State University'' 2: 23–35 n Russian; English translation in ''Selecta Mathematica Sovietica'' 1: 373–388, 1981 * R. I. Bogdanov (1979). "Versal deformations of singular points of vector fields on a plane," ''Functional Analysis and Its Applications'' 13: 63–64 n Russian; English translation available * R. I. Bogdanov (2003). ''Nonlinear Dynamical Systems on a Plane and Their Applications'', Vuzovskaya Kniga Publishing House, Moscow

References

* Math-Net.Ru/Person

Accessed on September 29, 2007. * Home pages of the Skobeltsyn Institute of Nuclear Physic

and Tsiolkovskii State Technological Universit

Accessed on September 29, 2007. * Web site of Russia's Genealogical Tre

Accessed on September 29, 2007.
Mention of Rifkat Bogdanov's death
1950 births 2013 deaths Tatar people of Russia Soviet mathematicians 21st-century Russian mathematicians Tatar people from the Soviet Union {{Russia-academic-bio-stub

See also

Selected publications

References