PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1997 | 39 | 1 | 77-87
Tytuł artykułu

Symplectic Capacities in Manifolds

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Symplectic capacities coinciding on convex sets in the standard symplectic vector space are extended to any subsets of symplectic manifolds. It is shown that, using embeddings of non-smooth convex sets and a product formula, calculations of some capacities become very simple. Moreover, it is proved that there exist such capacities which are distinct and that there are star-shaped domains diffeomorphic to the ball but not symplectomorphic to any convex set.
Słowa kluczowe
Rocznik
Tom
39
Numer
1
Strony
77-87
Opis fizyczny
Daty
wydano
1997
Twórcy
  • Département de Mathématiques, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Suisse
Bibliografia
  • [A84] J. P. Aubin, L'analyse non linéaire et ses motivations économiques, Masson, Paris, 1984.
  • [CE80] F. H. Clarke, I. Ekeland, Hamiltonian trajectories with prescribed minimal period, Comm. Pure Appl. Math. 33 (1980), 103-116.
  • [E90] I. Ekeland, Convexity methods in Hamiltonian mechanics, Springer, Berlin-Heidelberg, 1990.
  • [EH89] I. Ekeland, H. Hofer, Symplectic Topology and Hamiltonian Dynamics I, Math. Z. 200 (1989), 355-378. See also C. R. Acad. Sci. Paris Sér. I Math. 307 (1988), 37-40.
  • [EH90] I. Ekeland, H. Hofer, Symplectic Topology and Hamiltonian Dynamics II, Math. Z. 203 (1990), 553-567.
  • [G85] M. Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307-347.
  • [H91] M. Herman, Exemples de flots Hamiltoniens dont aucune perturbation en topologie $C^\infty$ n'a d'orbites périodiques sur un ouvert de surfaces d'énergies, C. R. Acad. Sci. Sér. I Math. 312 (1991), 989-994.
  • [HZ87] H. W. Hofer, E. Zehnder, Periodic solutions on hypersurfaces and a result by C. Viterbo, Invent. Math. 90 (1987), 1-9.
  • [HZ90] H. W. Hofer, E. Zehnder, A new capacity for symplectic manifolds, in: Analysis et cetera, Academic Press, 1990, 405-429.
  • [HZ94] H. Hofer, E. Zehnder, Symplectic Invariants and Hamiltonian Dynamics, Birkhäuser, Basel-Boston-Berlin, 1994.
  • [K90] A. F. Künzle, Une capacité symplectique pour les ensembles convexes et quelques applications, Ph.D. thesis, Université Paris IX Dauphine, June 1990.
  • [K91] A. F. Künzle, The least characteristic action as symplectic capacity, preprint, Forschungsinstitut für Mathematik, ETH Zürich, May 1991.
  • [K93] A. F. Künzle, Singular Hamiltonian systems and Symplectic Capacities, in: Singularities and Differential Equations, Banach Center Publ. 33 (1996), 171-187.
  • [R70] R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton N.J., 1970.
  • [Si93] K. F. Siburg, Symplectic capacities in two dimensions, Manuscripta Math. 78 (1993), 149-163.
  • [Si90] J. C. Sikorav, Systèmes Hamiltoniens et topologie symplectique, Lecture Notes, Dipartimento di Matematica dell'Università di Pisa, August 1990.
  • [V87] C. Viterbo, A proof of the Weinstein conjecture in $ℝ^{2n}$, Ann. Inst. H. Poincaré Anal. Non Linéaire 4 (1987), 337-357.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv39z1p77bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.