Decoupling surface analysis of classical irregular scattering and clarification of its icicle structure

New developments in classical chaotic scattering

Classical chaotic scattering is a topic of fundamental interest in nonlinear physics due to the numerous existing applications in fields such as celestial mechanics, atomic and nuclear physics and fluid mechanics, among others. Many new advances in chaotic scattering have been achieved in the last few decades. This work provides a current overview of the field, where our attention has been mainly focused on the most important contributions related to the theoretical framework of chaotic scattering, the fractal dimension, the basins boundaries and new applications, among others. Numerical techniques and algorithms, as well as analytical tools used for its analysis, are also included. We also show some of the experimental setups that have been implemented to study diverse manifestations of chaotic scattering. Furthermore, new theoretical aspects such as the study of this phenomenon in time-dependent systems, different transitions and bifurcations to chaotic scattering and a classification of boundaries in different types according to symbolic dynamics are also shown. Finally, some recent progress on chaotic scattering in higher dimensions is also described.

Topological aspects of chaotic scattering in higher dimensions

We investigate the topological properties of the chaotic invariant set associated with the dynamics of scattering systems with three or more degrees of freedom. We show that the separation of one degree of freedom from the rest in the asymptotic regime, a common property in a large class of scattering models, defines a gate which is a dynamical object with phase space separating invariant manifolds. The manifolds form an invariant set causing singularities in the scattering process. The codimension one property of the manifolds ensures that the fractal structure of the invariant set can be studied by scattering functions defined over simple one-dimensional families of initial conditions as usually done in two-degree-of-freedom scattering problems. It is found that the fractal dimension of the invariant set is not due to the gates but to interior hyperbolic periodic orbits.

Chaotic scattering: An introduction

In recent years chaotic behavior in scattering problems has been found to be important in a host of physical situations. Concurrently, a fundamental understanding of the dynamics in these situations has been developed, and such issues as symbolic dynamics, fractal dimension, entropy, and bifurcations have been studied. The quantum manifestations of classical chaotic scattering is also an extremely active field, with new analytical techniques being developed and with experiments being carried out. This issue of Chaos provides an up-to-date survey of the range of work in this important field of study.

Chaotic electronic scattering with He(+)

We investigate classical electronic collisions with a He(+) ion. Scattering functions, such as the scattering angle, collisional time, or energy of the outgoing electron, all exhibit an interesting hierarchial self-similar structure, which can be interpreted in terms of the indefinite number of electronic returns to the vicinity of the nucleus, encounters between electrons, and Keplerian excursions of electrons during the collisional processes. Based on this mechanism a binary coding is introduced to organize the dynamics of this three-body system and to provide an understanding of the self-similarity among generations of scale magnification, which yields escape rates that vary with the sectional cut into the parameter space. The self-similarity displayed within a single generation, on the other hand, can be simply tied to the periods of the two independent electronic excursions. The physical interpretation and the symbolic dynamics introduced here are generally useful for three-body collisional systems, including atomic, molecular, or stellar collisions.