Valentin Afraimovich
Valentin Afraimovich (Russian: Валентин Сендерович Афраймович, born 2 April 1945 in Kirov, Kirov Oblast, USSR) is a Soviet, Russian and Mexican mathematician. He has made important contributions in a number of areas including dynamical systems theory, qualitative theory of ordinary differential equations, bifurcation theory, concept of attractor,[1] 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.[2]
Biography
He got his Ph.D. (Kandidat) degree in 1974 at the Nizhny Novgorod State University under the advise of L. P. Shil’nikov. Also in 1990 he received his Doctor of Science degree in Mathematics and Physics, at Saratov State University in Russia. Since then he has held several academic positions, including:
- 1992-1995 Visiting Principal Research Scientist, Georgia Institute of Technology, Atlanta.
- 1995-1996 Visiting Professor, Northwestern University, Evanston, IL.
- 1996-1998 Visiting Professor, National Tsing Hua University, Hsinchu, Taiwan.
- 1998–present Professor–researcher, IICO, Universidad Autónoma de San Luis Potosí, S.L.P., México.
Afraimovich's students include Mark Shereshevsky, Nizhny Novgorod 1990; Todd Ray Young, Atlanta, Georgia, 1995; Antonio Morante , San Luis Potosí (SLP) México, 2002; Salomé Murgia, SLP México, 2003; Alberto Cordonet, SLP Mexico, 2002; Francisco Ordaz, SLP Mexico, 2004; Leticia Ramirez, SLP Mexico, 2005; Irma Tristan-Lopez, SLP Mexico, 2010.
Selected scientific papers
- 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)[3]
- 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 [4][5]
- V. Afraimovich and T. Young, Relative density of irrational rotation numbers in families of circle di eomorphisms. 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, J. 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, V.S.; V.I. Arnold, et al. (1999). Bifurcation Theory And Catastrophe Theory. Springer. ISBN 3540653791.
- Afraimovich, V.S.; I. S. Aranson, M. I. Rabinovich. Multidimensional Strange Attractors and Turbulence. Harwood Academic. ISBN 3718648687.
- Afraimovich, V.S.; Sze-Bi Hsu. Lectures On Chaotic Dynamical Systems. Ams/Ip Studies In Advanced Mathematics. ISBN 0821831682.
- Afrajmovich, V.S.; V.I. Arnold, Yu S. Il'yashenko, L. P. Shil'nikov. Dynamical Systems V. Springer. ISBN 3540181733.
- Afraimovich, V.S.; V. I. Nekorkin, G. V. Osipov, V. D. Shalfeev. Stability, structures and chaos in nonlinear synchronization networks. ISBN 9789812798718.
- Afraimovich, V.S.; E. Ugalde and J. Urías (2006,). Fractal Dimensions for Poincaré Recurrences (Monograph Series on Nonlinear Sciences and Complexity Volume 2). Elsevier. ISBN 0444521895.
- Afraimovich, V.S. (2010,). Hamiltonian Chaos Beyond the KAM Theory. Springer. ISBN 978-3-642-12717-5.
- Afraimovich, V.S. (2010,). Long-range Interactions, Stochasticity and Fractional Dynamics. Springer. ISBN 978-3-642-12342-9.
- Афраймович, В.С.; Э. Угальде, Х. Уриас (2011). Фрактальные Размерности для Времен Возвращения Пуанкаре. R&C Dynamics, Russia. ISBN 978-5-93972-903-1.
See also
References
External links
| Persondata |
| Name |
Afraimovich, Valentin |
| Alternative names |
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| Short description |
Mathematician |
| Date of birth |
2 April 1945 |
| Place of birth |
Kirov, Kirov Oblast, Russia |
| Date of death |
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| Place of death |
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