The Morse index theorem for regular Lagrangian systems

Chaofeng Zhu

Contact the author: Please use for correspondence this email.
Submission date: 01. Jul. 2003
Pages: 30
Bibtex
MSC-Numbers: 34B05, 53C22, 58C50, 58E10, 70H05
PACS-Numbers: 02.40
Keywords and phrases: regular lagrangian system, index form, spectral flow, relative morse index, maslov index, maslov-type index
Download full preprint: PDF (306 kB), PS ziped (238 kB)

Abstract:
In this paper, we prove the Morse index theorem for the index forms of regular Lagrangian systems with selfadjoint boundary condition coming from variational problems. We then give the relationship of them under two different boundary conditions. The Morse index theorem for the corresponding second order selfadjoint differential operators will be proved in recent paper: B. Booss and C. Zhu, The general spectral flow formula.