본문 바로가기
HOME> 논문 > 논문 검색상세

논문 상세정보

Journal of the Korean Mathematical Society = 대한수학회지 v.42 no.1, 2005년, pp.65 - 83   피인용횟수: 2

NORMALIZATION OF THE HAMILTONIAN AND THE ACTION SPECTRUM

OH YONG-GEUN    (Department of Mathematics University of Wisconsin, and Korea Institute for Advanced Study  );
  • 초록

    In this paper, we prove that the two well-known natural normalizations of Hamiltonian functions on the symplectic manifold ( $M,\;{\omega}$ ) canonically relate the action spectra of different normalized Hamiltonians on arbitrary symplectic manifolds ( $M,\;{\omega}$ ). The natural classes of normalized Hamiltonians consist of those whose mean value is zero for the closed manifold, and those which are compactly supported in IntM for the open manifold. We also study the effect of the action spectrum under the ${\pi}_1$ of Hamiltonian diffeomorphism group. This forms a foundational basis for our study of spectral invariants of the Hamiltonian diffeomorphism in [8].


  • 주제어

    Hamiltonians .   normalization .   action functional .   action spectrum.  

  • 참고문헌 (17)

    1. I. Ekeland and H. Hofer, Symplectic topology and Hamiltonian dynamics I, Math. Z. 200, (1989), 355-378 
    2. M. Entov, K-area, Hofer metric and geometry of conjugacy classes in Lie groups, Invent. Math. 146 (2001), 93-141 
    3. A. Floer and H. Hofer, Symplectic homology I, Math. Z. 215 (1994), 37-88 
    4. H. Hofer, On the topological properties of symplectic maps, Proc. Roy. Soc. Edinburgh 115 (1990), 25-38 
    5. F. Lalonde, D. McDuff and L. Polterovich, Topological rigidity of Hamiltonian loops and quantum homology, Invent. Math. 135 (1999), 369-385 
    6. J. Marsden and J. Ratiu, Construction of spectral invariants of Hamiltonian paths on closed symplectic manifolds, in 'The Breadth of Stmplectic and Poisson Geometry', Progr. Math. 232 (2004), 525-570 ed., Birkhouser 
    7. Y.-G. Oh, Symplectic topology as the geometry of action functional, I, J. Differential Geom. 46 (1997), 499-577 
    8. Y.-G. Oh, Symplectic topology as the geometry of action functional, II, Comm. Anal. Geom. 7 (1999), 1-55 
    9. Y.-G. Oh, Chain level Floer theory and Hofer's geometry of the Hamiltonian dif- feomorphism group, Asian J. Math. 6 (2002), 799-830, math.SG/0104243 
    10. L. Polterovich, The Geometry of the Group of Symplectic Diffeomorphisms, Birkhauser, 2001 
    11. P. Rabinowitz, Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math. 31 (1978), 157-184 
    12. M. Schwarz, On the action spectrum for closed symplectically aspherical mani- folds, Pacific J. Math. 193 (2000), 419-461 
    13. P. Seidel, $\pi_1$ of symplectic diffeomorphism groups and invertibles in quantum homology rings, GAFA (1997), 1046-1095 
    14. C. Viterbo, Symplectic topology as the geometry of generating functions, Math. Ann. 292 (1992), 685-710 
    15. A. Banyaga, Sur la structure du groupe des diffeomorphismes qui preservent une forme symplectique, Comm. Math. Helv. 53 (1978), 174-227 
    16. I. Ekeland and H. Hofer, Symplectic topology and Hamiltonian dynamics II, Math. Z. 203, (1989), 553-569 
    17. A. Floer, Symplectic fixed points and holomorphic spheres, Comm. Math. Phys. 120 (1989), 575-611 
  • 이 논문을 인용한 문헌 (2)

    1. 2009. "" Journal of the Korean Mathematical Society = 대한수학회지, 46(2): 363~447     
    2. 2016. "" Journal of the Korean Mathematical Society = 대한수학회지, 53(4): 795~834     

 활용도 분석

  • 상세보기

    amChart 영역
  • 원문보기

    amChart 영역

원문보기

무료다운로드
유료다운로드
  • 원문이 없습니다.

유료 다운로드의 경우 해당 사이트의 정책에 따라 신규 회원가입, 로그인, 유료 구매 등이 필요할 수 있습니다. 해당 사이트에서 발생하는 귀하의 모든 정보활동은 NDSL의 서비스 정책과 무관합니다.

원문복사신청을 하시면, 일부 해외 인쇄학술지의 경우 외국학술지지원센터(FRIC)에서
무료 원문복사 서비스를 제공합니다.

NDSL에서는 해당 원문을 복사서비스하고 있습니다. 위의 원문복사신청 또는 장바구니 담기를 통하여 원문복사서비스 이용이 가능합니다.

이 논문과 함께 출판된 논문 + 더보기