The Poincaré-Bendixson Theorem: from Poincaré to the XXIst century
The Poincaré-Bendixson Theorem and the development of the theory are presented - from the papers of Poincaré and Bendixson to modern results.
The Poincaré-Bendixson Theorem and the development of the theory are presented - from the papers of Poincaré and Bendixson to modern results.
El concepto de curvatura es muy familiar en la Geometría Diferencial. En este artículo se procura mostrar tanto la evolución de su concepto a lo largo de la historia como alguna de sus aplicaciones. En esta exposición existe una limitación tanto en la presenatción de algunos tópicos como en la ausencia de otros que son básicos en la Geometría de Riemann. Entre éstos últimos cabría destacar, entre otros, las variedades minimales y las kählerianas o la teoría de Morse. Aunque de manera implícita,...
The present paper provides a test case for the significance of the historical category “structuralism” in the history of modern mathematics. We recapitulate the various approaches to the fundamental group present in Poincaré’s work and study how they were developed by the next generations in more “structuralist” manners. By contrasting this development with the late introduction and comparatively marginal use of the notion of fundamental groupoid and the even later consideration of equivalence relations...
We investigate an approach of Bass to study the Jacobian Conjecture via the degree of the inverse of a polynomial automorphism over an arbitrary ℚ-algebra.