Related papers: Order in extremal trajectories

In a recent Letter, Hunt and Ott argued that SHORT-period unstable periodic orbits (UPOs) would be the invariant sets associated with a chaotic attractor that are most likely to optimize the time average of some smooth scalar performance…

We prove the existence of an effective universal upper bound for the order of any integral periodic orbit of any integral algebraic dynamical system in a fixed ambient space. Using this, we demonstrate the decidability of periodicity in…

We study nonautonomous discrete dynamical systems with randomly perturbed trajectories. We suppose that such a system is generated by a sequence of continuous maps which converges uniformly to a map $f$. We give conditions, under which a…

A new type of asymptotic behavior in a game dynamics system is discovered. The system exhibits behavior which combines chaotic motion and attraction to heteroclinic cycles; the trajectory visits several unstable stationary states repeatedly…

We compute the dispersion laws of chaotic periodic systems using the semiclassical periodic orbit theory to approximate the trace of the powers of the evolution operator. Aside from the usual real trajectories, we also include complex…

We study the periodic orbits and the escapes in two different dynamical systems, namely (1) a classical system of two coupled oscillators, and (2) the Manko-Novikov metric (1992) which is a perturbation of the Kerr metric (a general…

The properties of long, numerically-determined periodic orbits of two low-dimensional chaotic systems, the Lorenz equations and the Kuramoto-Sivashinsky system in a minimal-domain configuration, are examined. The primary question is to…

We predict that continuously monitored quantum dynamics can be chaotic. The optimal paths between past and future boundary conditions can diverge exponentially in time when there is time-dependent evolution and continuous weak monitoring.…

We compare the divergence of orbits and the reversibility error for discrete time dynamical systems. These two quantities are used to explore the behavior of the global error induced by round off in the computation of orbits. The similarity…

In this paper, we implement a generalised pseudo-Newtonian potential to study the off-equatorial orbits inclined at a certain angle with the equatorial plane around Schwarzschild and Kerr-like compact object primaries surrounded by a…

We study fluctuations of the Wigner time delay for open (scattering) systems which exhibit mixed dynamics in the classical limit. It is shown that in the semiclassical limit the time delay fluctuations have a distribution that differs…

Grebogi, Ott and Yorke (Phys. Rev. A 38(7), 1988) have investigated the effect of finite precision on average period length of chaotic maps. They showed that the average length of periodic orbits ($T$) of a dynamical system scales as a…

We consider the stability of periodic map with period-$2$ in linear fractional difference equations where the function is $f(x)=ax$ at even times and $f(x)=bx$ at odd times. The stability of such a map for an integer order map depends on…

Here I review recent work, by other authors and by myself, on some particular topics related to the regular and chaotic motion in elliptical galaxies. I show that it is quite possible to build highly stable triaxial stellar systems that…

We present a new chaotic system of three coupled ordinary differential equations, limited to quadratic nonlinear terms. A wide variety of dynamical regimes are reported. For some parameters, chaotic reversals of the amplitudes are produced…

A multidimensional chaos is generated by a special initial value problem for the non-autonomous impulsive differential equation. The existence of a chaotic attractor is shown, where density of periodic solutions, sensitivity of solutions…

We present here a new method which applies well ordered symbolic dynamics to find unstable periodic and non-periodic orbits in a chaotic system. The method is simple and efficient and has been successfully applied to a number of different…

For chaotic classical systems, the distribution of return times to a small region of phase space is universal. We propose a simple tool to investigate multiple returns in quantum systems. Numerical evidence for the baker map and kicked top…

A procedure to characterize chaotic dynamical systems with concepts of complex networks is pursued, in which a dynamical system is mapped onto a network. The nodes represent the regions of space visited by the system, while edges represent…

By folding an autonomous system of rational equations in the plane to a scalar difference equation, we show that the rational system has coexisting periodic orbits of all possible periods as well as stable aperiodic orbits for certain…