The Role of Topology in Solving Differential Equations and its applications

Authors

  • Ms. Rinku Assistant Professor, Department of Mathematics Hindu Girls College Sonipat

Keywords:

Topology, Differential Equations, independent variables, physical or mathematical phenomena

Abstract

The role of topology in solving differential equations refers to the use of topological concepts and methods to study the behavior of solutions to differential equations. A differential equation is an equation that relates a function and its derivatives to some independent variables. The solutions to a differential equation are functions that satisfy the equation and describe some physical or mathematical phenomena.

References

K. Austin and J. T. Oden, "A Topological Approach to the Study of Differential Equations," Journal of Mathematical Analysis and Applications, vol. 64, no. 1, pp. 69-80, 1978.

M. W. Hirsch, S. Smale, and R. L. Devaney, Differential Equations, DynamicalSystems, and an Introduction to Chaos, 3rd ed., Elsevier, 2012.

J. Moser, "Stable and Random Motions in Dynamical Systems," Annals ofMathematics, vol. 77, no. 3, pp. 473-527, 1963.

D. Henry, Geometric Theory of Semilinear Parabolic Equations, Springer-Verlag,1981.

J. Palis and W. de Melo, Geometric Theory of Dynamical Systems: An Introduction,Springer-Verlag, 1982.

S. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology,Chemistry, and Engineering, 2nd ed., Westview Press, 2015.

G. Teschl, Ordinary Differential Equations and Dynamical Systems, AmericanMathematical Society, 2012.

R. Abraham and J. Marsden, Foundations of Mechanics, 2nd ed., Westview Press,1987.

J. M. Lee, Introduction to Smooth Manifolds, 2nd ed., Springer, 2013.

J. Milnor, Topology from the Differentiable Viewpoint, Princeton University Press,1965.

R. H. maps, "Topological Methods in the Theory of Differential Equations," Bulletinof the American Mathematical Society, vol. 83, no. 6, pp. 1119-1141, 1977.

J. K. Hunter and B. Nachtergaele, Applied Analysis, American Mathematical Society,2001.

E. R. Fadell and S. Husseini, Geometry and Topology of Configuration Spaces,Springer, 2001.

Downloads

Published

2022-03-30

How to Cite

Ms. Rinku. (2022). The Role of Topology in Solving Differential Equations and its applications. Innovative Research Thoughts, 8(1), 115–118. Retrieved from http://irt.shodhsagar.com/index.php/j/article/view/1111