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Singular Bohr–Sommerfeld rules for 2D integrable systems

Yves Colin de Verdière, San Vũ Ngọc (2003)

Annales scientifiques de l'École Normale Supérieure

Singular fibres of the momentum mapping for integrable Hamiltonian systems.

Horst Knörrer (1984)

Journal für die reine und angewandte Mathematik

Singular Hamiltonian systems and symplectic capacities

Alfred Künzle (1996)

Banach Center Publications

The purpose of this paper is to develop the basics of a theory of Hamiltonian systems with non-differentiable Hamilton functions which have become important in symplectic topology. A characteristic differential inclusion is introduced and its equivalence to Hamiltonian inclusions for certain convex Hamiltonians is established. We give two counterexamples showing that basic properties of smooth systems are violated for non-smooth quasiconvex submersions, e.g. even the energy conservation which nevertheless...

Sobre los sistemas mecánicos con enlaces.

Rafael Ramírez (1989)

Collectanea Mathematica

A mathematical model is proposed in order to describe the behaviour of mechanical systems with constraints.

Solutions d'équations d'Hamilton-Jacobi et géométrie symplectique

C. Viterbo (1995/1996)

Séminaire Équations aux dérivées partielles (Polytechnique)

Solutions of DEs and PDEs as potential maps using first order Lagrangians.

Udrişte, Constantin (2001)

Balkan Journal of Geometry and its Applications (BJGA)

Solutions périodiques de systèmes hamiltoniens

Henri Berestycki (1982/1983)

Séminaire Bourbaki

Some affine properties of the $k$ -symplectic manifolds.

Awane, A. (1998)

Beiträge zur Algebra und Geometrie

Some examples of nonsingular Morse-Smale vector fields on $S^{3}$

F. Wesley Wilson Jr (1977)

Annales de l'institut Fourier

One wonders or not whether it is possible to determine the homotopy class of a vector field by examining some algebraic invariants associated with its qualitative behavior. In this paper, we investigate the algebraic invariants which are usually associated with the periodic solutions of non-singular Morse-Smale vector fields on the 3-sphere. We exhibit some examples for which there appears to be no correlation between the algebraic invariants of the periodic solutions and the homotopy classes of...