Bi-Hamiltonian structure as a shadow of non-Noether symmetry.
Chavchanidze, G. (2003)
Georgian Mathematical Journal
A. Katok, D. Bernstein (1987)
Inventiones mathematicae
Stanisław Janeczko, Zbigniew Jelonek (2009)
Fundamenta Mathematicae
Let and be compact symplectic manifolds (resp. symplectic manifolds) of dimension 2n > 2. Fix 0 < s < n (resp. 0 < k ≤ n) and assume that a diffeomorphism Φ : X → Y maps all 2s-dimensional symplectic submanifolds of X to symplectic submanifolds of Y (resp. all isotropic k-dimensional tori of X to isotropic tori of Y). We prove that in both cases Φ is a conformal symplectomorphism, i.e., there is a constant c ≠0 such that .
Patrick Iglesias (1983)
Annales de l'I.H.P. Physique théorique
Alan Weinstein, Christpher B. Croke (1981)
Inventiones mathematicae
V. Benci (1984)
Annales de l'I.H.P. Analyse non linéaire
M. Francaviglia, D. Krupka (1985)
Annales de l'I.H.P. Physique théorique
M.A. Olshanetsky, A.M. perelomov (1976)
Inventiones mathematicae
Didier Robert, Bernard Helffer (1981)
Annales de l'institut Fourier
Dans cet article nous généralisons les résultats obtenus par J. Chazarain sur le spectre d’opérateurs de Schrödinger lorsque . Nous étendons ses résultats aux opérateurs pseudo-différentiels globalement elliptiques d’ordre .
Mitric, Gabriel (1997)
General Mathematics
Đorđe S. Đukić (1984)
Zbornik Radova
Mario Girardi, Michele Matzeu (1990)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
We prove some stability results for a certain class of periodic solutions of nonautonomous Hamiltonian systems in the case of Hamiltonian functions either with subquadratic growth or homogeneous with superquadratic growth. Thus we extend to the nonautonomous case some results recently established by the Authors for the autonomous case.
Krupková, O., Volný, P. (2006)
Lobachevskii Journal of Mathematics
L. Chierchia, G. Gallavotti (1994)
Annales de l'I.H.P. Physique théorique
P. Iglesias (1983)
Annales de l'I.H.P. Physique théorique
Ernesto A. Lacomba, J. Guadalupe Reyes (2000)
Publicacions Matemàtiques
A mistake was found in the reasoning leading to a Lagrangian which we considered as equivalent from the formula for the action S(γ) below the classical mechanical problem (3) on "Non singular Hamiltonian systems and geodesic flows on surfaces with negative curvature", page 271.
Xingyong Zhang, Xianhua Tang (2012)
Applications of Mathematics
The existence of solutions for boundary value problems for a nonlinear discrete system involving the -Laplacian is investigated. The approach is based on critical point theory.
M.A. Olshanetsky, A.M. Perelomov (1979)
Inventiones mathematicae
H. Hofer, K. Wysocki (1990)
Mathematische Annalen
Azzouz Awane (2008)
Revista Matemática Complutense