Related papers: Cusp-scaling behavior in fractal dimension of chao…
We investigate the topological properties of invariant sets associated with the dynamics of scattering systems with three or more degrees of freedom. We show that the asymptotic separation of one degree of freedom from the rest in the…
This article treats chaotic scattering with three degrees of freedom, where one of them is open and the other two are closed, as a first step toward a more general understanding of chaotic scattering in higher dimensions. Despite of the…
A class of simplified measures is constructed to capture the key features of generic spatio-temporally chaotic systems. A combined analytical and numerical investigation allows us to extablish the scaling beahviour of the fractal dimension…
Numerical bifurcation analysis, and in particular two-parameter continuation, is used in consort with numerical simulation to reveal complicated dynamics in the Mackey-Glass equation for moderate values of the delay close to the onset of…
We analyze situations where a saddle-node bifurcation occurs on a fractal basin boundary. Specifically, we are interested in what happens when a system parameter is slowly swept in time through the bifurcation. Such situations are known to…
In the parameter spaces of nonlinear dynamical systems, we investigate the boundaries between periodicity and chaos and unveil the existence of fractal sets characterized by a singular fractal dimension. This dimension stands out from the…
We shall use symmetry breaking as a tool to attack the problem of identifying the topology of chaotic scatteruing with more then two degrees of freedom. specifically we discuss the structure of the homoclinic/heteroclinic tangle and the…
We study the pattern of activated trajectories in a double well system without detailed balance, in the weak noise limit. The pattern may contain cusps and other singular features, which are similar to the caustics of geometrical optics.…
Quasiperiodic systems offer an appealing intermediate between long-range ordered and genuine disordered systems, with unusual critical properties. One-dimensional models that break the so-called self-dual symmetry usually display a mobility…
We show that weak dissipation, typical in realistic situations, can have a metamorphic consequence on nonhyperbolic chaotic scattering in the sense that the physically important particle-decay law is altered, no matter how small the amount…
Experiments observing the liquid surface in a vertically oscillating container have indicated that modeling the dynamics of such systems require maps that admit states at infinity. In this paper we investigate the bifurcations in such a…
Traditional studies of chaos in conservative and driven dissipative systems have established a correspondence between sensitive dependence on initial conditions and fractal basin boundaries, but much less is known about the relation between…
We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space, focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…
Chaotic scattering is a manifestation of transient chaos realized by the scattering with non-integrable potential. When the initial position is taken in the potential, a particle initially exhibits chaotic motion, but escapes outside after…
The precise theoretical characterization of a fractionalized phase in spatial dimensions higher than one is through the concept of ``topological order''. We describe a physical effect that is a robust and direct consequence of this hidden…
We explore the concept of scaling invariance in a type of dynamical systems that undergo a transition from order (regularity) to disorder (chaos). The systems are described by a two-dimensional, nonlinear mapping that preserves the area in…
We show that chiral order in two-dimensional nonreciprocal flocking mixtures is generically unstable. Combining large-scale agent-based simulations with a coarse-grained continuum description, we demonstrate that rotating chiral states…
Multifractality of charged particle pseudorapidity distributions is analyzed in central collisions of carbon and copper nuclei at 4.5 GeV/c per nucleon. Within the method of normalized factorial moments, modified to remove the bias of…
We investigate the dynamics of passive particles in a two-dimensional incompressible open flow composed of a fixed topographical point vortex and a background current with a periodic component. The tracer dynamics is found to be typically…
We investigate the connections between microscopic chaos, defined on a dynamical level and arising from collisions between molecules, and diffusion, characterized by a mean square displacement proportional to the time. We use a number of…