Bifurcation of stationary and heteroclinic orbits for parametrized gradient-like flows

Thomas Bartsch

Banach Center Publications (1996)

  • Volume: 35, Issue: 1, page 9-27
  • ISSN: 0137-6934

How to cite


Bartsch, Thomas. "Bifurcation of stationary and heteroclinic orbits for parametrized gradient-like flows." Banach Center Publications 35.1 (1996): 9-27. <>.

author = {Bartsch, Thomas},
journal = {Banach Center Publications},
keywords = {Conley index theory; minimax theory; bifurcation theory},
language = {eng},
number = {1},
pages = {9-27},
title = {Bifurcation of stationary and heteroclinic orbits for parametrized gradient-like flows},
url = {},
volume = {35},
year = {1996},

AU - Bartsch, Thomas
TI - Bifurcation of stationary and heteroclinic orbits for parametrized gradient-like flows
JO - Banach Center Publications
PY - 1996
VL - 35
IS - 1
SP - 9
EP - 27
LA - eng
KW - Conley index theory; minimax theory; bifurcation theory
UR -
ER -


  1. [Ba1] T. Bartsch, On the genus of representation spheres, Comment. Math. Helv. 65 (1990), 85-95. Zbl0704.57024
  2. [Ba2] T. Bartsch, Topological Methods for Variational Problems with Symmetries, Lecture Notes in Math. 1560, Springer, Berlin Heidelberg 1993. 
  3. [Ba3] T. Bartsch, A generalization of the Weinstein-Moser theorems on periodic orbits of a Hamiltonian system near an equilibrium, preprint, Heidelberg 1994. 
  4. [Ba4] T. Bartsch, Bifurcation theorey for nonlinear eigenvalue problems, in preparation. 
  5. [BaC] T. Bartsch and M. Clapp, Bifurcation theory for symmetric potential operators and the equivariant cup-length, Math. Z. 204 (1990), 341-356. Zbl0682.58037
  6. [Be] V. Benci, A geometrical index for the group S 1 and some applications to the study of periodic solutions of ordinary differential equations, Commun. Pure Appl. Math. 34 (1981), 393-432. Zbl0447.34040
  7. [Bö] R. Böhme, Die Lösung der Verzweigungsgleichungen für nichtlineare Eigenwertprobleme, Math. Z. 127 (1972), 105-126. Zbl0254.47082
  8. [CaS] S. E. Capell and J. L. Shaneson, Nonlinear similarity, Ann. of Math. 113 (1981), 315-355. 
  9. [Co] C. Conley, Isolated Invariant Sets and the Morse Index, CBMS, Regional Conf. Ser. in Math. 38, AMS Providence, R.I., 1978. 
  10. [CZ] C. Conley and E. Zehnder, Morse type index theory for flows and periodic solutions for Hamiltonian systems, Comm. Pure Appl. Math. 37 (1984), 207-253. Zbl0559.58019
  11. [tD] T. tom Dieck, Transformation Groups, de Gruyter, Berlin 1987. 
  12. [D] A. Dold, Lectures on Algebraic Topology, Grundlehren der math. Wiss. 200, Springer, Berlin Heidelberg 1980. 
  13. [FR1] E. Fadell and P. H. Rabinowitz, Bifurcation for odd potential operators and an alternative topological index, J. Funct. Anal. 26 (1977), 48-67. Zbl0363.47029
  14. [FR2] E. Fadell and P. H. Rabinowitz, Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems, Inv. Math. 45 (1978), 139-174. Zbl0403.57001
  15. [K] M. A. Krasnoselski, On special coverings of a finite-dimensional sphere, Dokl. Akad. Nauk SSSR 103 (1955), 966-969 (in Russian). 
  16. [Ma] A. Marino, La biforcazione nel caso variationale, Confer. Sem. Mat. Univ. Bari 132 (1977). 
  17. [MW] J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, Springer, New York 1989. 
  18. [R1] P. H. Rabinowitz, A bifurcation theorem for potential operators, J. Funct. Anal. 25 (1977), 412-424. Zbl0369.47038
  19. [R2] P. H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS, Regional Conf. Ser. in Math. 65, AMS, Providence, R.I., 1986. 
  20. [Sa] D. Salamon, Connected simple systems and the Conley index of isolated invariant sets, Trans. Amer. Math. Soc. 291 (1985), 1-41. Zbl0573.58020
  21. [Sp] E. Spanier, Algebraic Topology, McGraw-Hill, New York 1966. 
  22. [Y] C. T. Yang, On the theorems of Borsuk-Ulam, Kakutani-Yamabe-Yujòbô and Dyson, Ann. Math. 60 (1954), 262-282. Zbl0057.39104

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.