| comment
| - L'analyse globale est une branche des mathématiques qui traite des problèmes globaux d'analyse. Elle fait appel pour cela à des notions de topologie (topologie générale, topologie différentielle, topologie algébrique, topologie géométrique, théorie des espaces vectoriels topologiques), de géométrie différentielle et d'analyse fonctionnelle. L'analyse globale a pour première caractéristique, par rapport à l'analyse locale, de faire appel à des concepts non linéaires, étant donné qu'un espace vectoriel (de dimension finie) n'est que l'approximation locale d'une variété différentielle. D'où le rôle prédominant que joue la géométrie différentielle en analyse globale, qui est une synthèse de l'analyse classique et de la géométrie. Les variétés considérées sont souvent des variétés de fonctions,
- In mathematics, global analysis, also called analysis on manifolds, is the study of the global and topological properties of differential equations on manifolds and vector bundles. Global analysis uses techniques in infinite-dimensional manifold theory and topological spaces of mappings to classify behaviors of differential equations, particularly nonlinear differential equations. These spaces can include singularities and hence catastrophe theory is a part of global analysis. Optimization problems, such as finding geodesics on Riemannian manifolds, can be solved using differential equations so that the calculus of variations overlaps with global analysis. Global analysis finds application in physics in the study of dynamical systems and topological quantum field theory.
- Em matemática, a análise global, também chamada de análise em variedades, é o estudo das propriedades globais e topológicas das equações diferenciais em variedades e fibrados vetoriais.A análise global usa técnicas em teoria de variedades infinitas e espaços topológicos de mapeamentos para classificar comportamentos de equações diferenciais, particularmente equações diferenciais não lineares. Esses espaços podem incluir singularidades e, portanto, a teoria da catástrofe faz parte da análise global. Problemas de otimização, como encontrar geodésicas em variedades Riemannianas, podem ser resolvidos usando equações diferenciais para que o cálculo das variações se sobreponha à análise global. A análise global encontra aplicação na física no estudo de sistemas dinâmicos e na teoria quântica de
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| dbo:abstract
| - In mathematics, global analysis, also called analysis on manifolds, is the study of the global and topological properties of differential equations on manifolds and vector bundles. Global analysis uses techniques in infinite-dimensional manifold theory and topological spaces of mappings to classify behaviors of differential equations, particularly nonlinear differential equations. These spaces can include singularities and hence catastrophe theory is a part of global analysis. Optimization problems, such as finding geodesics on Riemannian manifolds, can be solved using differential equations so that the calculus of variations overlaps with global analysis. Global analysis finds application in physics in the study of dynamical systems and topological quantum field theory.
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