User:Paquitotrek
Valentin Afraimovich ([] Error: {{Langx}}: no text (help), born 2 April 1945 in Kirov, 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, 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.
Biography
[edit]He got his Ph.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 the same Nizhny Novgorod State University in Russia. Since then he has held several academic positions, for example (for the last years):
- 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, Nizhnyi Novgorod 1990; Tod Ray Young, Atlanta Georgia, 1995; Antonio Morante , San Luis Potosi (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, SLP Mexico, 2010.
Selected Scientific papers
[edit]- V. Afraimovich, L. Glebsky, Measures Related To 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, 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)[1]
- 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 [2] [3]
- 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
[edit]- V. S. Afrajmovich, V. I. Arnold, et al., Bifurcation Theory And Catastrophe Theory, ISBN 3540653791
- V. S. Afraimovich, I. S. Aranson, M. I. Rabinovich, Multidimensional Strange Attractors and Turbulence, Harwood Academic, ISBN 3718648687
- V. Afraimovich, Lectures On Chaotic Dynamical Systems (Ams/Ip Studies In Advanced Mathematics), ISBN 0821831682
- V. S. Afrajmovich, V. Arnold, Yu S. Il'yashenko, L. P. Shil'nikov, Dynamical Systems V, Springer, ISBN 3540181733
- V. S. Afraimovich, V. I. Nekorkin, G. V. Osipov, V. D. Shalfeev, Stability, structures and chaos in nonlinear synchronization networks, ISBN 9789812798718
See also
[edit]
- Dynamical systems
- Homoclinic Orbit
- Topology
- Chaos theory
- Attractor
- Bifurcation theory
- Catastrophe theory
References
[edit]
External links
[edit]
- Other works
- Personal web page
- Conference celebrating Afraimovich's 65th aniversary
- List of some publications
- American Institute of Mathematical Sciences
- A super short curriculum vitae
- Paquitotrek at the Mathematics Genealogy Project