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It is shown that for particles moving in a plane under the action of attracting central potentials and a perturbing force (potential but not central),orbits representing the falling down of the particle to the center of force exist.texto impreso
Escape to infinity is proved to occur when a charge moves under the action of the magnetic field created by a finite number of planar closed wires.texto impreso
The frontiers of boundedness F(b) of the orbits of dynamical systems X defined on R(n) are studied. When X is completely integrable some topological properties of F(b) are found and, in certain cases, F(b) is localized with the help of symmetrie[...]texto impreso
It is shown that under certain conditions the limit speed of electric charges moving in a space of type R-n of dimension one or two, under isotropic friction, is preserved under some perturbations. These results hold when relativistic equations [...]texto impreso
Díaz-Cano Ocaña, Antonio ; Gonzalez Gascón, F. ; Peralta Salas, Daniel | American Institute of Physics | 2006Dynamical systems on R-n presenting geometric chaos, i.e., open domains where bounded and unbounded orbits are intermingled, have been constructed. The opposite situation (open scattering) has been studied for integrable Hamiltonian and non-Hami[...]texto impreso
The study of the stability of a periodic solution p of a vector field using either the linear variational equations (associated to the vector field at p ), or the Poincaré map on a cross section, is known to present some difficulties. This work[...]texto impreso
Submersions f such that f(-1)(0) contains a given fiber F, and that are invariant under a family of vector fields s leaving F invariant, are constructed. Examples for which a submersion of this kind cannot exist are also given. In the absence of[...]texto impreso
By an application of the geometrical techniques of Lie, Cohen, and Dickson it is shown that a system of differential equations of the form [x^(r_i)]_i = F_i; (where r_i > 1 for every i = 1 , ... ,n) cannot admit an infinite number of pointlike [...]texto impreso
By an application of the geometrical techniques of Lie, Cohen, and Dickson it is shown that a system of differential equations of the form [x^(r_i)]_i = F_i(where r_i > 1 for every i = 1 , ... ,n) cannot admit an infinite number of pointlike sy[...]
