On the chaotic behavior and the non-integrability of the four vortices problem
On the Dynamic Behaviour of Chebyshev Polynomials.
On the structure of the space of continuous maps with zero topological entropy
One-dimensional and two-dimensional dynamics of cubic maps.
Optimal, adaptive and single state feedback control for a 3D chaotic system with golden proportion equilibria
In this paper, the problems on purposefully controlling chaos for a three-dimensional quadratic continuous autonomous chaotic system, namely the chaotic Pehlivan-Uyaroglu system are investigated. The chaotic system, has three equilibrium points and more interestingly the equilibrium points have golden proportion values, which can generate single folded attractor. We developed an optimal control design, in order to stabilize the unstable equilibrium points of this system. Furthermore, we propose...
Outer boundaries of self-similar tiles.
Periodic orbits of renormalisation for the correlations of strange nonchaotic attractors.
Periodic points and chaotic-like dynamics of planar maps associated to nonlinear Hill's equations with indefinite weight.
Phase multistability of synchronous chaotic oscillations.
Phase synchronization in coupled Sprott chaotic systems presented by fractional differential equations.
Points périodiques d’applications birationnelles de
Nous donnons une condition suffisante pour l’existence de points périodiques pour une application birationnelle de . Sous cette hypothèse, une estimation précise du nombre de points périodiques de période fixée est obtenue. Nous donnons une application de ce résultat à l’étude dynamique de ces applications, en calculant explicitement l’auto-intersection de leur courant invariant naturellement associé. Nos résultats reposent essentiellement sur le théorème de Bézout donnant le cardinal de l’intersection...
Potentials unbounded below.
Quelques propriétés des lignes critiques d'une récurrence du second ordre à inverse non unique. Détermination d'une zone absorbante
Random mappings with a single absorbing center and combinatorics of discretizations of the logistic mapping.
Recurrent point set of the shift on Σ and strong chaos
Let (Σ,ϱ) be the one-sided symbolic space (with two symbols), and let σ be the shift on Σ. We use A(·), R(·) to denote the set of almost periodic points and the set of recurrent points respectively. In this paper, we prove that the one-sided shift is strongly chaotic (in the sense of Schweizer-Smítal) and there is a strongly chaotic set 𝒥 satisfying 𝒥 ⊂ R(σ)-A(σ).
Representations of the Whitehead manifold and Julia sets
Robust controller design for modified projective synchronization of Chen-Lee chaotic systems with nonlinear inputs.
Scaling properties of a hybrid Fermi-Ulam-bouncer model.
Singular strange attractors on the boundary of Morse-Smale systems
Sliding mode observers and observability singularity in chaotic synchronization.