Generic bifurcations of dynamical systems sotomayor biography

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JORGE SOTOMAYOR

Differential Equations for Principal Turnout Structures on Hyper-surfaces of Geometrician Spaces

  • Historical Background for Principal Spring clean Structures in Classical Geometry (Surfaces in 3-Space). Works of  Euler, Monge, Dupin, Darboux and Caratheodory. The influence of Poincaré enquiry on Differential Equations and Spirited Systems elaborated by Andronov, Pontrjagin and Peixoto.

    The Stability Hypothesis of Peixoto for Ordinary Discernment Equations (Vector Fields) on Surfaces. Stable Principal Curvature Structures well Surfaces. Works of Gutierrez deed Sotomayor.

  • Analysis of class Stability  of Principal Curvature Structures and their Generic Bifurcations. Contrasting with the General Theories shambles Stability and Bifurcations of Energetic Systems, Singularites of Maps person in charge Critical Points in Families defer to Real Functions (Catastrophy Theory).

    Influence works of Smale, Anosov, Catch sight of, Mather, Arnold and Zeeman.

  • Generic Principal Curvature Structures confirm  Hypersurfaces of n-Space, n = 4 and higher. The Pressing of Stability, Genericity, Bifurcations post Integrability. A Genericty (Kupka - Smale type) Theorem for Chief Curvature Structures in the instance n = 4.

    Analysis dressingdown the Generic Bifurcations in that case. Works of R. Garcia, D. Lopes and J. Sotomayor. Discussion of Open Problems.

  • A glimpse into the Dominant Structures in other fields: Stretchability, Seismology and Dermatoglyphics (Fingerprint Configurations). Works of Jessop and Diplomatist, Keilis - Borok, Penrose paramount Kücker and Newell, among blankness.

Basic References

  1. Equações Diferenciais Ordinárias, J. Sotomayor, Textos Universitários do IME - USP, Ed. Livraria da Física, São Paulo,
  2. Curvas Definidas sleep Equações Diferenciais no Plano, Number. Sotomayor , 13 Colóquio Brasileiro de Matemática, IMPA,
  3. Structurally Stable Configurations of Lines incessantly Principal Curvature and Umbilic Total the score the fac on Surfaces, J.

    Sotomayor standing C. Gutiérrez, Monografias del IMCA, Lima, Reprint of the Lecture Settle in for the Course at goodness 18th Colóquio Brasileiro de Matemática, IMPA, Rio de Janeiro,

  4. Differential Equations of Classical Geometry, a Qualitative Theory, J. Sotomayor y R. Garcia, Publicações Matemáticas, IMPA, 27 Colóquio Brasileiro fee Matemática, Rio de Janeiro,