2007 Conference on Variational and Topological Methods: Theory, Applications, Numerical Simulations, and Open Problems. Electron. J. Diff. Eqns., Conference 18 (2010), pp. 45-56.

A geometric approach to invariant sets for dynamical systems

David Medina, Pablo Padilla

In this article, we present a geometric framework to study invariant sets of dynamical systems associated with differential equations. This framework is based on properties of invariant sets for an area functional. We obtain existence results for heteroclinic and periodic orbits. We also implement this approach numerically by means of the steepest descent method.

Published July 10, 2010.
Math Subject Classifications: 37L05.
Key Words: Invariant sets; dynamical systems; area functional; steepest descent method.

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David Medina
Instituto Tecnológico Superior de Perote
Carretera Perote-México km. 2.5
Centro, Perote, Veracruz, C. P. 91270, México
email: medina@math.unam.mx
  Pablo Padilla
Departamento de Matemáticas y Mecánica, IIMAS-UNAM
Apartado Postal 20-726, C. P. 01000 México, México
email: pablo@mym.iimas.unam.mx

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