By performing a systematic study of the Hénon map, we find low-period sinks for parameter values extremely close to the classical ones. This raises the question whether or not the well-known Hénon attractor-the attractor of the Hénon map existing for the classical parameter values-is a strange attractor, or simply a stable periodic orbit. Using results from our study, we conclude that even if t...

We discuss one parameter families of unimodal maps, with negative Schwarzian derivative, unfolding a saddle-node bifurcation. It was previously shown that for a parameter set of positive Lebesgue density at the bifurcation, the maps possess attracting periodic orbits of high period. We show that there is also a parameter set of positive density at the bifurcation, for which the maps exhibit abs...

Invariant sets embedded in a chaotic attractor can generate time averages that diier from the average generated by typical orbits on the attractor. Motivated by two diierent topics (namely, controlling chaos and riddled basins of attraction), we consider the question of which invariant set yields the largest (optimal) value of an average of a given smooth function of the system state. We presen...

The existence and Hausdorff dimension of the global attractor for discretization of a damped wave equation with the periodic nonlinearity under the periodic boundary conditions are studied for any space dimension. The obtained Hausdorff dimension is independent of the mesh sizes and the space dimension and remains small for large damping, which conforms to the physics.

The full nonlinear dissipative quasigeostrophic model is shown to have a unique temporally almost periodic solution when the wind forcing is temporally almost periodic under suitable constraints on the spatial square–integral of the wind forcing and the β parameter, Ekman number, viscosity and the domain size. The proof involves the pullback attractor for the associated nonautonomous dynamical ...

Synopsis. A purely combinatorial procedure for nding an isolating neighbourhood and an index pair contained in a given set being a nite union of cubes in R s is presented. It is applied for a computer-assisted computation of the Conley index of an isolated invariant subset of the Henon attractor. As a corollary, it is shown that the Henon attractor contains periodic orbits of all principal peri...

We consider the solutions lying on the global attractor of the two-dimensional Navier–Stokes equations with periodic boundary conditions and analytic forcing. We show that in this case the value of a solution at a finite number of nodes determines elements of the attractor uniquely, proving a conjecture due to Foias and Temam. Our results also hold for the complex Ginzburg–Landau equation, the ...

We report our results on non-periodic experimental time series of pressure in a spark ignition engine. The experiments were performed for a low rotational velocity of a crankshaft and a relatively large spark advance angle. We show that the combustion process has many chaotic features. Surprisingly, the reconstructed attractor has a characteristic butterfly shape similar to a chaotic attractor ...

We examine a strange chaotic attractor and its unstable periodic orbits in case of one degree of freedom nonlinear oscillator with non symmetric potential. We propose an efficient method of chaos control stabilizing these orbits by a pulsive feedback technique. Discrete set of pulses enable us to transfer the system from one periodic state to another.