Off-center reflections: caustics and chaos.
On a one-dimensional analogue of the Smale horseshoe
We construct a transformation T:[0,1] → [0,1] having the following properties: 1) (T,|·|) is completely mixing, where |·| is Lebesgue measure, 2) for every f∈ L¹ with ∫fdx = 1 and φ ∈ C[0,1] we have , where μ is the cylinder measure on the standard Cantor set, 3) if φ ∈ C[0,1] then for Lebesgue-a.e. x.
On almost specification and average shadowing properties
We study relations between the almost specification property, the asymptotic average shadowing property and the average shadowing property for dynamical systems on compact metric spaces. We show implications between these properties and relate them to other important notions such as shadowing, transitivity, invariant measures, etc. We provide examples showing that compactness is a necessary condition for these implications to hold. As a consequence, we also obtain a proof that limit shadowing in...
On chaotic dynamics in rational polygonal billiards.
On geometric detection of periodic solutions and chaotic dynamics.
On periodic orbits in discrete-time cascade systems.
On quadratic symplectic mappings.
On small stochastic perturbations of mappings of the unit interval
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 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.