PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1991-1992 | 56 | 2 | 195-211
Tytuł artykułu

Equivariant maps of joins of finite G-sets and an application to critical point theory

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A lower estimate is proved for the number of critical orbits and critical values of a G-invariant C¹ function $f:S^n → ℝ$, where G is a finite nontrivial group acting freely and orthogonally on $ℝ^{n+1} \ {0}$. Neither Morse theory nor the minimax method is applied. The proofs are based on a general version of Borsuk's Antipodal Theorem for equivariant maps of joins of G-sets.
Rocznik
Tom
56
Numer
2
Strony
195-211
Opis fizyczny
Daty
wydano
1992
otrzymano
1991-02-15
poprawiono
1991-03-30
poprawiono
1991-11-12
Twórcy
  • Institute of Mathematics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
Bibliografia
  • [1] T. Bartsch, Critical orbits of invariant functionals and symmetry breaking, For- schungsschwerpunkt Geometrie, Universität Heidelberg, Heft Nr 34, 1988.
  • [2] V. Benci and F. Pacella, Morse theory for symmetric functionals on the sphere and an application to a bifurcation problem, Nonlinear Anal. 9 (1985), 763-771.
  • [3] G. Bredon, Introduction to Compact Transformation Groups, Academic Press, 1972.
  • [4] S. N. Chow and J. K. Hale, Methods of Bifurcation Theory, Springer, 1982.
  • [5] K. Deimling, Nonlinear Functional Analysis, Springer, 1985.
  • [6] E. Fadell and P. H. Rabinowitz, Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems, Invent. Math. 45 (1978), 139-174.
  • [7] A. Granas and J. Dugundji, Fixed Point Theory, PWN, Warszawa 1982.
  • [8] M. Hall, The Theory of Groups, Macmillan, New York 1959.
  • [9] W. Krawcewicz and W. Marzantowicz, Lusternik-Schnirelmann method for functionals invariant with respect to a finite group action, preprint, 1988.
  • [10] W. Krawcewicz and W. Marzantowicz, Some remarks on the Lusternik-Schnirelmann method for non-differentiable functionals invariant with respect to a finite group action, preprint, 1988.
  • [11] J. Milnor, Construction of universal bundles, II, Ann. of Math. 63 (1956), 430-436.
  • [12] R. S. Palais, Critical point theory and the minimax principle, in: Proc. Sympos. Pure Math. 15, Amer. Math. Soc., 1970, 185-212.
  • [13] R. S. Palais, Lusternik-Schnirelmann theory on Banach manifolds, Topology 5 (1966), 115-132.
  • [14] P. H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, CBMS Regional Conf. Ser. in Math. 65, Amer. Math. Soc., 1984.
  • [15] V. A. Rokhlin and D. B. Fuks, An Introductory Course in Topology. Geometric Chapters, Nauka, Moscow 1977 (in Russian).
  • [16] J. A. Wolf, Spaces of Constant Curvature, University of California, Berkeley, Calif., 1972.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv56z2p195bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.