On the C⁰-closing lemma
A proof of the C⁰-closing lemma for noninvertible discrete dynamical systems and its extension to the noncompact case are presented.
On the classical and quantum evolution of lagrangian half-forms in phase space
On the classical non-integrability of the Hamiltonian system for hydrogen atoms in crossed electric and magnetic fields
Hydrogen atoms placed in external fields serve as a paradigm of a strongly coupled multidimensional Hamiltonian system. This system has been already very extensively studied, using experimental measurements and a wealth of theoretical methods. In this work, we apply the Morales-Ramis theory of non-integrability of Hamiltonian systems to the case of the hydrogen atom in perpendicular (crossed) static electric and magnetic uniform fields.
On the concentration of solutions of singularly perturbed Hamiltonian systems in .
On the Conley index in Hilbert spaces - a multivalued case
We introduce the cohomological Conley type index theory for multivalued flows generated by vector fields which are compact and convex-valued perturbations of some linear operators.
On the construction of a -counterexample to the Hamiltonian Seifert conjecture in .
On the density of the range for some nonlinear operators
On the existence and non-existence of closed trajectories for some Hamiltonian flows.
On the existence of equations of evolution.
On the existence of homoclinic points
On the existence of homoclinic solutions for almost periodic second order systems
On the Exponential Bound of the Cutoff Resolvent
A simpler proof of a result of Burq [1] is presented.
On the finite blocking property
A planar polygonal billiard is said to have the finite blocking property if for every pair of points in there exists a finite number of “blocking” points such that every billiard trajectory from to meets one of the ’s. Generalizing our construction of a counter-example to a theorem of Hiemer and Snurnikov, we show that the only regular polygons that have the finite blocking property are the square, the equilateral triangle and the hexagon. Then we extend this result to translation surfaces....
On the geometric structure of the set of solutions of Einstein equations [Book]
On the growth of averaged Weyl sums for rigid rotations
On the index theorem for symplectic orbifolds
We give an explicit construction of the trace on the algebra of quantum observables on a symplectiv orbifold and propose an index formula.
On the KAM - Theory Conditions for the Kirchhoff Top
* Partially supported by Grant MM523/95 with Ministry of Science and Technologies.In this paper the classical Kirchhoff case of motion of a rigid body in an infinite ideal fluid is considered. Then for the corresponding Hamiltonian system on the zero integral level, the KAM theory conditions are checked. In contrast to the known similar results, there exists a curve in the bifurcation diagram along which the Kolmogorov’s condition vanishes for certain values of the parameters.
On the -instability and -controllability of steady flows of an ideal incompressible fluid
In the existing stability theory of steady flows of an ideal incompressible fluid, formulated by V. Arnold, the stability is understood as a stability with respect to perturbations with small in vorticity. Nothing has been known about the stability under perturbation with small energy, without any restrictions on vorticity; it was clear that existing methods do not work for this (the most physically reasonable) class of perturbations. We prove that in fact, every nontrivial steady flow is unstable...
On the Lagrange-Souriau form in classical field theory
The Euler-Lagrange equations are given in a geometrized framework using a differential form related to the Poincare-Cartan form. This new differential form is intrinsically characterized; the present approach does not suppose a distinction between the field and the space-time variables (i.e. a fibration). In connection with this problem we give another proof describing the most general Lagrangian leading to identically vanishing Euler-Lagrange equations. This gives the possibility to have a geometric...
On the mechanics with noncontinuous hamiltonians