Obtuse triangular billiards. I: Near the triangle.
On -tensor fields on symplectic manifolds
Two symplectic structures on a manifold determine a (1,1)-tensor field on . In this paper we study some properties of this field. Conversely, if is (1,1)-tensor field on a symplectic manifold then using the natural lift theory we find conditions under which , is symplectic.
On a conjecture for the critical behaviour of KAM tori.
On a horizontal structure on differentiable manifolds
On a “mysterious” case of a quadratic Hamiltonian.
On a theorem of Chekanov
A proof of the Chekanov theorem is discussed from a geometric point of view. Similar results in the context of projectivized cotangent bundles are proved. Some applications are given.
On Anosov energy levels of convex Hamiltonian systems.
On Arnold's conjecture for symplectic fixed points
On chaotic dynamics in rational polygonal billiards.
On classical intrinsically resonant formal perturbation theory
On classical -matrix for the Kowalevski gyrostat on .
On classical series expansions for quasi-periodic motions.
On computer-aided solving differential equations and stability study of markets.
On control theory and its applications to certain problems for Lagrangian systems. On hyperimpulsive motions for these. II. Some purely mathematical considerations for hyper-impulsive motions. Applications to Lagrangian systems
See Summary in Note I. First, on the basis of some results in [2] or [5]-such as Lemmas 8.1 and 10.1-the general (mathematical) theorems on controllizability proved in Note I are quickly applied to (mechanic) Lagrangian systems. Second, in case , and satisfy conditions (11.7) when is a polynomial in , conditions (C)-i.e. (11.8) and (11.7) with -are proved to be necessary for treating satisfactorily 's hyper-impulsive motions (in which positions can suffer first order discontinuities)....
On control theory and its applications to certain problems for Lagrangian systems. On hyper-impulsive motions for these. III. Strengthening of the characterizations performed in parts I and II, for Lagrangian systems. An invariance property.
In [1] I and II various equivalence theorems are proved; e.g. an ODE with a scalar control is linear w.r.t. iff its solution with given initial conditions (chosen arbitrarily) is continuous w.r.t. in a certain sense, or iff
On critical points for noncoercive functionals and subharmonic solutions of some Hamiltonian systems.
On D’Alembert’s Principle
A formulation of the D’Alembert principle as the orthogonal projection of the acceleration onto an affine plane determined by nonlinear nonholonomic constraints is given. Consequences of this formulation for the equations of motion are discussed in the context of several examples, together with the attendant singular reduction theory.
On dissipative phenomena of the interaction of Hamiltonian systems.
On Elliptic Lower Dimensional Tori in Hamiltonian Systems.
On embedding the 1:1:2 resonance space in a Poisson manifold.