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On the application of control theory to certain problems for Lagrangian systems, and hyper-impulsive motion for these. I. Some general mathematical considerations on controllizable parameters

Aldo Bressan (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In applying control (or feedback) theory to (mechanic) Lagrangian systems, so far forces have been generally used as values of the control u ⁢ ( ⋅ ) . However these values are those of a Lagrangian co-ordinate in various interesting problems with a scalar control u = u ⁢ ( ⋅ ) , where this control is carried out physically by adding some frictionless constraints. This pushed the author to consider a typical Lagrangian system Σ , referred to a system χ of Lagrangian co-ordinates, and to try and write some handy conditions,...

On the C⁰-closing lemma

Anna A. Kwiecińska (1996)

Annales Polonici Mathematici

A proof of the C⁰-closing lemma for noninvertible discrete dynamical systems and its extension to the noncompact case are presented.

On the classical non-integrability of the Hamiltonian system for hydrogen atoms in crossed electric and magnetic fields

Robert Gębarowski (2011)

Banach Center Publications

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 finite blocking property

Thierry Monteil (2005)

Annales de l’institut Fourier

A planar polygonal billiard 𝒫 is said to have the finite blocking property if for every pair ( O , A ) of points in 𝒫 there exists a finite number of “blocking” points B 1 , ⋯ , B n such that every billiard trajectory from O to A meets one of the B i ’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 index theorem for symplectic orbifolds

Boris Fedosov, Bert-Wolfang Schulze, Nikolai Tarkhanov (2004)

Annales de l’institut Fourier

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

Christov, Ognyan (1997)

Serdica Mathematical Journal

* 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 L 2 -instability and L 2 -controllability of steady flows of an ideal incompressible fluid

Alexander Shnirelman (1999)

Journées équations aux dérivées partielles

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 L 2 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...

Currently displaying 501 – 520 of 912