Free Access
Volume 13, Number 3, July-September 2007
Page(s) 598 - 621
Published online 26 July 2007
  1. R. Abraham and J.E. Marsden, Foundations of Mechanics, 2nd edition. Benjamin/Cummings, Ink. Massachusetts (1978). [Google Scholar]
  2. L. Andersson and R. Howard, Comparison and rigidity theorems in Semi-Riemannian geometry. Comm. Anal. Geom. 6 (1998) 819–877. [MathSciNet] [Google Scholar]
  3. S.B. Angenent and R. van der Vorst, A priori bounds and renormalized Morse indices of solutions of an elliptic system. Ann. Inst. H. Poincaré Anal. Non Linéaire 17 (2000) 277–306. [CrossRef] [MathSciNet] [Google Scholar]
  4. V.I. Arnol'd, Sturm theorems and symplectic geometry. Funktsional. Anal. i Prilozhen. 19 (1985) 1–10. [Google Scholar]
  5. J.K. Beem, P.E. Ehrlich and K.L. Easley, Global Lorentzian Geometry. Mercel Dekker, Inc. New York and Basel (1996). [Google Scholar]
  6. V. Benci, F. Giannoni and A. Masiello, Some properties of the spectral flow in semiriemannian geometry. J. Geom. Phys. 27 (1998) 267–280. [CrossRef] [MathSciNet] [Google Scholar]
  7. A.L. Besse, Manifolds all of whose geodesics are closed. Ergebnisse der Mathematik und ihrer Grenzgebiete 93, Springer-Verlag (1978). [Google Scholar]
  8. O. Bolza, Lectures on Calculus of Variation. Univ. Chicago Press, Chicago (1904). [Google Scholar]
  9. S.E. Cappell, R. Lee and E.Y. Miller, On the Maslov index. Comm. Pure Appl. Math. 47 (1994) 121–186. [CrossRef] [MathSciNet] [Google Scholar]
  10. I. Chavel, Riemannian geometry: a modern introduction, in Cambridge tracts in Mathematics 108, Cambridge Univerisity Press (1993). [Google Scholar]
  11. P. Chossat, D. Lewis, J.P. Ortega and T.S. Ratiu, Bifurcation of relative equilibria in mechanical systems with symmetry. Adv. Appl. Math. 31 (2003) 10–45. [CrossRef] [Google Scholar]
  12. C. Conley and E. Zehnder, The Birhoff-Lewis fixed point theorem and a conjecture of V.I. Arnold. Invent. Math. 73 (1983) 33–49. [CrossRef] [MathSciNet] [Google Scholar]
  13. M. Crabb and I. James, Fibrewise Homotopy Theory. Springer-Verlag (1998). [Google Scholar]
  14. M. Daniel, An extension of a theorem of Nicolaescu on spectral flow and Maslov index. Proc. Amer. Math. Soc. 128 (1999) 611–619. [CrossRef] [Google Scholar]
  15. K. Deimling, Nonlinear Functional Analysis. Springer-Verlag (1985). [Google Scholar]
  16. I. Ekeland, Convexity methods in Hamiltonian systems. Ergebnisse der Mathematik und ihrer Grenzgebiete 19, Springer-Verlag, Berlin (1990). [Google Scholar]
  17. Guihua Fei, Relative Morse index and its application to Hamiltonian systems in the presence of symmetries. J. Diff. Eq. 122 (1995) 302–315. [CrossRef] [Google Scholar]
  18. P.M. Fitzpatrick and J. Pejsachowicz, Parity and generalized multiplicity. Trans. Amer. Math. Soc. 326 (1991) 281–305. [CrossRef] [MathSciNet] [Google Scholar]
  19. P.M. Fitzpatrick, J. Pejsachowicz and L. Recht, Spectral flow and bifurcation of critical points of strongly-indefinite functional. Part I. General theory. J. Funct. Anal. 162 (1999) 52–95. [CrossRef] [MathSciNet] [Google Scholar]
  20. P.M. Fitzpatrick, J. Pejsachowicz and L. Recht, Spectral flow and bifurcation of critical points of strongly-indefinite functional. Part II. Bifurcation of periodic orbits of Hamiltonian systems. J. Differ. Eq. 161 (2000) 18–40. [CrossRef] [Google Scholar]
  21. A. Floer, Relative Morse index for the symplectic action. Comm. Pure Appl. Math. 41 (1989) 335–356. [CrossRef] [Google Scholar]
  22. I.M. Gel'fand and S.V. Fomin, Calculus of Variations. Prentic-Hall Inc., Englewood Cliffs, New Jersey, USA (1963). [Google Scholar]
  23. I.M. Gel'fand and V.B. Lidskii, On the structure of the regions of stability of linear canonical systems of differential equations with periodic coefficients. Amer. Math. Soc. Transl. Ser. 2 8 (1958) 143–181. [Google Scholar]
  24. R. Giambó, P. Piccione and A. Portaluri, On the Maslov Index of Lagrangian paths that are not transversal to the Maslov cycle. Semi-Riemannian index Theorems in the degenerate case. (2003) Preprint. [Google Scholar]
  25. A.D. Helfer, Conjugate points on space like geodesics or pseudo self-adjoint Morse-Sturm-Liouville systems. Pacific J. Math. 164 (1994) 321–340. [MathSciNet] [Google Scholar]
  26. J. Jost, X. Li-Jost and X.W. Peng, Bifurcation of minimal surfaces in Riemannian manifolds. Trans. Amer. Math. Soc. 347 (1995) 51–62. [CrossRef] [MathSciNet] [Google Scholar]
  27. T. Kato, Perturbation Theory for linear operators. Grundlehren der Mathematischen Wissenschaften 132, Springer-Verlag (1980). [Google Scholar]
  28. W. Klingenberg, Closed geodesics on Riemannian manifolds. CBMS Regional Conference Series in Mathematics 53 (1983). [Google Scholar]
  29. W. Klingenberg, Riemannian Geometry. de Gruyter, New York (1995). [Google Scholar]
  30. M.A. Krasnoselskii, Topological methods in the theory of nonlinear integral equations. Pergamon, New York (1964). [Google Scholar]
  31. D.N. Kupeli, On conjugate and focal points in semi-Riemannian geometry. Math. Z. 198 (1988) 569–589. [CrossRef] [MathSciNet] [Google Scholar]
  32. S. Lang, Differential and Riemannian Manifolds. Springer-Verlag (1995). [Google Scholar]
  33. E. Meinrenken, Trace formulas and Conley-Zehnder index. J. Geom. Phys. 13 (1994) 1–15. [CrossRef] [MathSciNet] [Google Scholar]
  34. J. Milnor, Morse theory. Based on lecture notes by M. Spivak and R. Wells. Annals of Mathematics Studies 51, Princeton University Press, Princeton, N.J. (1963). [Google Scholar]
  35. M. Musso, J. Pejsachowicz and A. Portaluri, A Morse Index Theorem and bifurcation for perturbed geodesics on Semi-Riemannian Manifolds. Topol. Methods Nonlinear Anal. 25 (2005) 69–99. [MathSciNet] [Google Scholar]
  36. B. O'Neill, Semi-Riemannian geometry with applications to relativity. Academic Press, New York (1983). [Google Scholar]
  37. R.S. Palais, Foundations of global non-linear analysis. W.A. Benjamin, Inc., New York (1968). [Google Scholar]
  38. G. Peano, Lezioni di Analisi infinitesimale, Volume I, pp. 120–121, Volume II, pp. 187–195. Tipografia editrice G. Candeletti, Torino (1893). [Google Scholar]
  39. P. Piccione, A. Portaluri and D.V. Tausk, Spectral flow, Maslov index and bifurcation of semi-Riemannian geodesics. Ann. Global Anal. Geometry 25 (2004) 121–149. [CrossRef] [Google Scholar]
  40. A. Portaluri, A formula for the Maslov index of linear autonomous Hamiltonian systems. (2004) Preprint. [Google Scholar]
  41. A. Portaluri, Morse Index Theorem and Bifurcation theory on semi-Riemannian manifolds. Ph.D. thesis (2004). [Google Scholar]
  42. P.J. Rabier, Generalized Jordan chains and two bifurcation theorems of Krasnosel'skii. Nonlinear Anal. 13 (1989) 903–934. [CrossRef] [MathSciNet] [Google Scholar]
  43. J. Robbin and D. Salamon, The Maslov index for paths. Topology 32 (1993) 827-844. [CrossRef] [MathSciNet] [Google Scholar]
  44. J. Robbin and D. Salamon, The spectral flow and the Maslov index. Bull. London Math. Soc. 27 (1995) 1–33. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.