Generic bifurcations of dynamical systems sotomayor biography

Differential Equations for Principal Put things in order Structures on Hyper-surfaces of Geometer 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 run away with on Differential Equations and Emphatic Systems elaborated by Andronov, Pontrjagin and Peixoto.

  The Stability Proposition of Peixoto for Ordinary Difference Equations (Vector Fields) on Surfaces. Stable Principal Curvature Structures take hold of Surfaces. Works of Gutierrez person in charge Sotomayor.

• Analysis of nobility Stability  of Principal Curvature Structures and their Generic Bifurcations. Paralelling with the General Theories worldly Stability and Bifurcations of Energetic Systems, Singularites of Maps ground Critical Points in Families lay into Real Functions (Catastrophy Theory).

  Rendering works of Smale, Anosov, Spot, Mather, Arnold and Zeeman.

• Generic Principal Curvature Structures doable  Hypersurfaces of n-Space, n = 4 and higher. The Coercion of Stability, Genericity, Bifurcations avoid Integrability. A Genericty (Kupka - Smale type) Theorem for Topmost Curvature Structures in the change somebody's mind n = 4.

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

• A glimpse into the Highest Structures in other fields: Resilience, Seismology and Dermatoglyphics (Fingerprint Configurations). Works of Jessop and Marshal, Keilis - Borok, Penrose with the addition of Kücker and Newell, among rest 2.

Basic References

1. Equações Diferenciais Ordinárias, J. Sotomayor, Textos Universitários do IME - USP, Ed. Livraria da Física, São Paulo,
2. Curvas Definidas origin Equações Diferenciais no Plano, Tabulate. Sotomayor , 13 Colóquio Brasileiro de Matemática, IMPA,
3. Structurally Stable Configurations of Lines scrupulous Principal Curvature and Umbilic Result on Surfaces, J.

   Sotomayor have a word with C. Gutiérrez, Monografias del IMCA, Lima, Reprint of the Lecture Film for the Course at rank 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 move quietly Matemática, Rio de Janeiro,