On symmetries and invariant solutions of a coupled KdV system with variable coefficients.
On systems governed by two alternating vector fields
We investigate the nonautonomous periodic system of ODE’s of the form , where is a -periodic function defined by for , for and the vector fields and are related by an involutive diffeomorphism.
On tame embeddings of solenoids into 3-space
Solenoids are inverse limits of the circle, and the classical knot theory is the theory of tame embeddings of the circle into 3-space. We make a general study, including certain classification results, of tame embeddings of solenoids into 3-space, seen as the "inverse limits" of tame embeddings of the circle. Some applications in topology and in dynamics are discussed. In particular, there are tamely embedded solenoids Σ ⊂ ℝ³ which are strictly achiral. Since solenoids are non-planar,...
On the accessible points in the Julia sets of some entire functions
We prove that for some families of entire functions whose Julia set is the complement of the basin of attraction every branch of a tree of preimages starting from this basin is convergent.
On the algebraic hull of an automorphism group of a principal bundle.
On the anti–synchronization detection for the generalized Lorenz system and its applications to secure encryption
In this paper, a modified version of the Chaos Shift Keying (CSK) scheme for secure encryption and decryption of data will be discussed. The classical CSK method determines the correct value of binary signal through checking which initially unsynchronized system is getting synchronized. On the contrary, the new anti-synchronization CSK (ACSK) scheme determines the wrong value of binary signal through checking which already synchronized system is loosing synchronization. The ACSK scheme is implemented...
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
In applying control (or feedback) theory to (mechanic) Lagrangian systems, so far forces have been generally used as values of the control . However these values are those of a Lagrangian co-ordinate in various interesting problems with a scalar control , where this control is carried out physically by adding some frictionless constraints. This pushed the author to consider a typical Lagrangian system , referred to a system of Lagrangian co-ordinates, and to try and write some handy conditions,...
On the arithmetic sum of regular Cantor sets
On the attractors of Feigenbaum maps
A solution of the Feigenbaum functional equation is called a Feigenbaum map. We investigate the likely limit set (i.e. the maximal attractor in the sense of Milnor) of a non-unimodal Feigenbaum map, prove that it is a minimal set that attracts almost all points, and then estimate its Hausdorff dimension. Finally, for every s ∈ (0,1), we construct a non-unimodal Feigenbaum map with a likely limit set whose Hausdorff dimension is s.
On the Bautin bifurcation for systems of delay differential equations.
On the bifurcation set of complex polynomial with isolated singularities at infinity
On the Birkhoff normal form of a completely integrable hamiltonian system near a fixed point with resonance
On the -stability conjecture
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 capacity of a continuum with a non-dense orbit under a hyperbolic toral automorphism
On the chaotic behavior and the non-integrability of the four vortices problem
On the characterization of Hankel and Toeplitz operators describing switched linear dynamic systems with point delays.
On the classes of Lipschitz and smooth conjugacies of unimodal maps
Under very mild assumptions, any Lipschitz continuous conjugacy between the closures of the postcritical sets of two C¹-unimodal maps has a derivative at the critical point, and also on a dense set of its preimages. In a more restrictive situation of infinitely renormalizable maps of bounded combinatorial type the Lipschitz condition automatically implies the C¹-smoothness of the conjugacy. Here the critical degree can be any real number α > 1.
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.