Madison, WI 53706, USA
Department of Mathematics, University of Wisconsin-Madison
Rabinowitz P. H.
Gluing a Mountain Pass Solution to a Minimum
2009, vol. 14, no. 1, pp. 163-178
This paper presents a variational method for constructing solutions of a pendulum model equation that shadow a mountain pass solution glued to a minimum of the associated functional. It allows for more degenerate situations and gives more qualitative information than the classical Poincare–Birkho–Smale theory.
Bolotin S. V., Rabinowitz P. H.
Heteroclinic Geodesics for a Class of Manifolds With Symmetry
1998, vol. 3, no. 4, pp. 49-62
The results of Morse and Hedlund about minimal heteroclinic geodesics on surfaces are generalized to a class of Finsler manifolds possessing a symmetry. The existence of minimal heteroclinic geodesics is established. Under an assumption that the set of such geodesics has certain compactness properties, multibump chaotic geodesics are constructed.