# Global analysis

*https://en.wikipedia.org/wiki/Global_analysis*

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.^{
[1]}^{
[2]} Global analysis uses techniques in infinite-dimensional manifold theory and topological spaces of mappings to classify behaviors of differential equations, particularly nonlinear differential equations.^{
[3]} 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^{
[4]} and
topological quantum field theory.

## Journals

## See also

- Atiyah–Singer index theorem
- Geometric analysis
- Lie groupoid
- Pseudogroup
- Morse theory
- Structural stability
- Harmonic map

## References

**^**Smale, S. (January 1969). "What is Global Analysis".*American Mathematical Monthly*.**76**(1): 4–9. doi: 10.2307/2316777.**^**Richard S. Palais (1968).*Foundations of Global Non-Linear Analysis*(PDF). W.A. Benjamin, Inc.**^**Andreas Kriegl and Peter W. Michor (1991).*The Convenient Setting of Global Analysis*(PDF). American Mathematical Society. pp. 1–7. ISBN 0-8218-0780-3.**^**Marsden, Jerrold E. (1974).*Applications of global analysis in mathematical physics*. Berkeley, CA.: Publish or Perish, Inc. p. Chapter 2. ISBN 0-914098-11-X.