Related papers: Analytical study of chaos and applications
Relationships between a chaotic behavior and closely related properties of topological transitivity, sensitivity to initial conditions, density of closed orbits of homeomorphism groups and their countable products are investigated. We…
The dynamics of hexagon patterns in rotating systems are investigated within the framework of modified Swift-Hohenberg equations that can be considered as simple models for rotating convection with broken up-down symmetry, e.g.…
We study the interplay between regular and chaotic dynamics at the critical point of a generic first-order quantum phase transition in an interacting boson model of nuclei. A classical analysis reveals a distinct behavior of the coexisting…
We study the regular or chaotic character of orbits in a 3D dynamical model, describing a triaxial galaxy surrounded by a spherical dark halo component. Our numerical experiments suggest that the percentage of chaotic orbits decreases…
Phase mixing of chaotic orbits exponentially distributes these orbits through their accessible phase space. This phenomenon, commonly called ``chaotic mixing'', stands in marked contrast to phase mixing of regular orbits which proceeds as a…
We study the orbital structure of a self-consistent N-body equilibrium configuration of a barred galaxy constructed from cosmological initial conditions. The value of its spin parameter L is near the observed value of our Galaxy L=0.22. We…
We report on the application of chaos control to the irregular motion of an electron under the combined influence of a Coulomb and a magnetic field, the so-called ``diamagnetic Kepler problem'' (DKP). We show how to stabilize the classical…
The Melnikov method is applied to periodically perturbed open systems modeled by an inverse--square--law attraction center plus a quadrupolelike term. A compactification approach that regularizes periodic orbits at infinity is introduced.…
The method of restricted path integrals allows one to effectively consider continuous (prolonged in time) measurements of quantum systems. Monitoring of the system coordinates is such a continuous measurement that allows one to describe a…
Energy level statistics of quantized chaotic systems have been evaluated in the semiclassical limit via their periodic orbits using the Gutzwiller and related trace formulae. Here we evaluate a spectral statistic of chaotic 4-regular…
The chaotic or ordered character of orbits in galactic models is an important issue, since it can influence dynamical evolution. This distinction can be achieved with the help of the Smaller Alingment Index - (SALI). We describe here…
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.…
Chaotic hyperbolic dynamical systems enjoy a surprising degree of rigidity, a fact which is well known in the mathematics community but perhaps less so in theoretical physics circles. Low-dimensional hyperbolic systems are either conjugate…
Many exo-solar systems discovered in the last decade consist of planets orbiting in resonant configurations and consequently, their evolution should show long-term stability. However, due to the mutual planetary interactions a multi-planet…
The chaotic properties of simple two-dimensional rotation-translation models are explored and simulated. The models are given in difference equation forms, while the corresponding differential equations systems are studied and the resulting…
The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there…
Chaotic dynamics is always characterized by swarms of unstable trajectories, unpredictable individually, and thus generally studied statistically. It is often the case that such phase-space densities relax exponentially fast to a limiting…
After a general discussion of the thermodynamics of conductive processes, we introduce specific observables enabling the connection of the diffusive transport properties with the microscopic dynamics. We solve the case of Brownian…
The collective behavior of a coupled map lattice having {\it unbounded} chaotic local dynamics is investigated through the properties of its mean field. The presence of unstable periodic orbits in the local maps determines the emergence of…
Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…