Maslov index for homoclinic orbits of Hamiltonian systems

  • Chao-Nien Chen

    Department of Mathematics, National Changhua University of Education, Changhua, Taiwan, ROC
  • Xijun Hu

    Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing 100080, PR China

Abstract

A useful tool for studying nonlinear differential equations is index theory. For symplectic paths on bounded intervals, the index theory has been completely established, which revealed tremendous applications in the study of periodic orbits of Hamiltonian systems. Nevertheless, analogous questions concerning homoclinic orbits are still left open. In this paper we use a geometric approach to set up Maslov index for homoclinic orbits of Hamiltonian systems. On the other hand, a relative Morse index for homoclinic orbits will be derived through Fredholm index theory. It will be shown that these two indices coincide.

Cite this article

Chao-Nien Chen, Xijun Hu, Maslov index for homoclinic orbits of Hamiltonian systems. Ann. Inst. H. Poincaré Anal. Non Linéaire 24 (2007), no. 4, pp. 589–603

DOI 10.1016/J.ANIHPC.2006.06.002