Global bifurcation of fixed points and the poincaré translation operator on manifolds

Annali di Matematica Pura ed Applicata

Volumn 173, Issue 1, 1997, Pages 313-331

  Furi, Massimo ^a   Pera, Maria Patrizia ^a  

^a UNIVERSITY OF FLORENCE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 26444519413     PISSN: 03733114     EISSN: 16181891     Source Type: Journal    
DOI: 10.1007/BF01783474     Document Type: Article

References (14)

1. ALEXANDER J. C., A primer on connectivity, Proc. Conf. on Fixed Point Theory 1980, edited by E. Fadell and G. Fournier, Lecture Notes in Math., 886, Springer-Verlag, Berlin (1981), pp. 455-483.
2. BARTSCH T., A global index for bifurcation of fixed points, J. Reine Angew. Math., 391 (1988), pp. 181-197.
3. BROWN R. F., The Lefschetz Fixed Point Theorem, Scott, Foresman and Company, Glenview, Illinois (1971).
4. FURI M. - PERA M. P., A continuation principle for forced oscillations on differentiable manifolds, Pacific J. Math., 121 (1986), pp. 321-338.
5. FURI M. - PERA M.P., The forced spherical pendulum does have forced oscillations, in Delay Differential Equations and Dynamical Systems, Busenberg S. and Martelli M. Editors, Lecture Notes in Math., 1475, Springer-Verlag, Berlin, 1991, pp. 176-183.
6. FURI M. - PERA M. P., A continuation principle for periodic solutions of forced motion equations on manifolds and applications to bifurcation theory, Pacific J. Math., 160 (1993), pp. 219-244.
7. GRANAS A., The Leray-Schauder index and the fixed point theory for arbitrary ANR's, Bull. Soc. Math. France, 100 (1972), pp. 209-228.
8. GUILLEMIN V. - POLLACK A., Differential Topology, Prentice-Hall Inc., Englewood Cliffs, New Jersey (1974).
9. HIRSCH M. W., Differential Topology, Graduate Texts in Math., Vol. 33, Springer-Verlag, Berlin (1976).
10. KRASNOSEL'SKII M. A., The Operator of Translation along the Trajectories of Differential Equations, Transl. Math. Monographs, Vol. 19, Amer. Math. Soc., Providence, Rhode Island (1968).
11. LANG S., Introduction to Differentiable Manifolds, John Wiley & Sons Inc., New York (1966).
12. MILNOR J. W., Topology from the Differentiable Viewpoint, Univ. Press of Virginia, Charlottesville (1965).
13. NUSSBAUM R. D., The fixed point index and fixed point theorems, in Topological Methods for Ordinary Differential Equations, Lecture Notes in Math., 1537, Springer-Verlag, Berlin (1993), pp. 143-205.
14. TROMBA A. J., The Euler characteristic of vector fields on Banach manifolds and a globalization of Leray-Schauder degree, Advances Math., 28 (1978), pp. 148-173.